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Published: 9 March 2023
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1

Drábek, Pavel. "Landesman-Lazer type condition and nonlinearities with linear growth." Czechoslovak Mathematical Journal 40, no. 1 (1990): 70–86. http://dx.doi.org/10.21136/cmj.1990.102360.

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2

Tomiczek, Petr. "Periodic Problem with a Potential Landesman Lazer Condition." Boundary Value Problems 2010, no. 1 (2010): 586971. http://dx.doi.org/10.1155/2010/586971.

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3

Sanni, Sikiru Adigun. "On the Weak Solution of a Semilinear Boundary Value Problem without the Landesman-Lazer Condition." International Journal of Differential Equations 2011 (2011): 1–13. http://dx.doi.org/10.1155/2011/801706.

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4

Tomiczek, Petr. "The Duffing equation with the potential Landesman–Lazer condition." Nonlinear Analysis: Theory, Methods & Applications 70, no. 2 (January 2009): 735–40. http://dx.doi.org/10.1016/j.na.2008.01.006.

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5

Rezende, M. C. M., P. M. Sánchez-Aguilar, and E. A. B. Silva. "A Landesman–Lazer Local Condition for Semilinear Elliptic Problems." Bulletin of the Brazilian Mathematical Society, New Series 50, no. 4 (February 22, 2019): 889–911. http://dx.doi.org/10.1007/s00574-019-00132-5.

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6

Drábek, Pavel. "Landesman-Lazer condition for nonlinear problems with jumping nonlinearities." Journal of Differential Equations 85, no. 1 (May 1990): 186–99. http://dx.doi.org/10.1016/0022-0396(90)90095-7.

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7

Papageorgiou, Nikolaos S., Calogero Vetro, and Francesca Vetro. "Landesman-Lazer type (p, q)-equations with Neumann condition." Acta Mathematica Scientia 40, no. 4 (June 5, 2020): 991–1000. http://dx.doi.org/10.1007/s10473-020-0408-y.

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8

Ma, Sheng, Zhihua Hu, Jing Jin, and Qin Jiang. "Some existence theorems for semilinear Neumann problems with Landesman-Lazer condition revisited." Filomat 34, no. 2 (2020): 339–50. http://dx.doi.org/10.2298/fil2002339m.

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In this paper, existence theorems are established for Neumann problems for semilinear elliptic equations at resonance together with Landesman-Lazer condition revisited. Our existence results follow as an application of the Saddle point Theorem together with a standard eigenspace decomposition.
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9

Cimatti, Giovanni. "A Landesman-Lazer type condition for a nonlinear Stekloff Problem." Nonlinear Differential Equations and Applications NoDEA 14, no. 5-6 (December 2007): 729–38. http://dx.doi.org/10.1007/s00030-007-5055-7.

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10

Li, Jin, Jianlin Luo, and Zaihong Wang. "RETRACTED ARTICLE: PERIODIC SOLUTIONS OF SECOND ORDER IMPULSIVE DIFFERENTIAL EQUATIONS AT RESONANCE VIA VARIATIONAL APPROACH." Mathematical Modelling and Analysis 19, no. 5 (November 1, 2014): 664–75. http://dx.doi.org/10.3846/13926292.2014.980864.

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In this paper, we study the existence of periodic solutions of second order impulsive dierential equations at resonance. We prove the existence of periodic solutions under a generalized Landesman{Lazer type condition by using variational method.
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11

Amster, P., and P. De Nápoli. "A nonlinear second order problem with a nonlocal boundary condition." Abstract and Applied Analysis 2006 (2006): 1–11. http://dx.doi.org/10.1155/aaa/2006/38532.

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We study a nonlinear problem of pendulum-type for ap-Laplacian with nonlinear periodic-type boundary conditions. Using an extension of Mawhin's continuation theorem for nonlinear operators, we prove the existence of a solution under a Landesman-Lazer type condition. Moreover, using the method of upper and lower solutions, we generalize a celebrated result by Castro for the classical pendulum equation.
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12

Drabek, Pavel, and Martina Langerova. "Landesman-Lazer condition revisited: the influence of vanishing and oscillating nonlinearities." Electronic Journal of Qualitative Theory of Differential Equations, no. 68 (2015): 1–11. http://dx.doi.org/10.14232/ejqtde.2015.1.68.

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13

Santanilla, Jairo. "Solvability of a nonlinear boundary value problem without Landesman-Lazer condition." Nonlinear Analysis: Theory, Methods & Applications 13, no. 6 (January 1989): 683–93. http://dx.doi.org/10.1016/0362-546x(89)90087-4.

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14

Kannan, R., J. J. Nieto, and M. B. Ray. "A class of nonlinear boundary value problems without Landesman-Lazer condition." Journal of Mathematical Analysis and Applications 105, no. 1 (January 1985): 1–11. http://dx.doi.org/10.1016/0022-247x(85)90093-9.

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15

Han, Zhiqing. "Solvability of Elliptic Boundary Value Problems without Standard Landesman-Lazer Condition." Acta Mathematica Sinica, English Series 16, no. 2 (April 2000): 349–60. http://dx.doi.org/10.1007/s101140000054.

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16

Han, Zhiqing. "Solvability of Elliptic Boundary Value Problems without Standard Landesman-Lazer Condition." Acta Mathematica Sinica 16, no. 2 (April 1, 2000): 349–60. http://dx.doi.org/10.1007/s101140050014.

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17

Fonda, Alessandro, and Maurizio Garrione. "A Landesman–Lazer-type condition for asymptotically linear second-order equations with a singularity." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 142, no. 6 (November 27, 2012): 1263–77. http://dx.doi.org/10.1017/s0308210511000151.

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We consider the T-periodic problemwhere g: [0,T]×]0,+∞[→ℝ exhibits a singularity of a repulsive type at the origin, and an asymptotically linear behaviour at infinity. In particular, for large x, g(t, x) is controlled from both sides by two consecutive asymptotes of the T-periodic Fučik spectrum, with possible equality on one side. Using a suitable Landesman–Lazer-type condition, we prove the existence of a solution.
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18

Iannacci, R., and M. N. Nkashama. "Nonlinear Two Point Boundary Value Problems at Resonance Without Landesman-Lazer Condition." Proceedings of the American Mathematical Society 106, no. 4 (August 1989): 943. http://dx.doi.org/10.2307/2047278.

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19

Iannacci, R., and M. N. Nkashama. "Nonlinear two-point boundary value problems at resonance without Landesman-Lazer condition." Proceedings of the American Mathematical Society 106, no. 4 (April 1, 1989): 943. http://dx.doi.org/10.1090/s0002-9939-1989-1004633-9.

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20

Ha, C. W. "On the Solvability of an Operator Equation without the Landesman-Lazer Condition." Journal of Mathematical Analysis and Applications 178, no. 2 (September 1993): 547–52. http://dx.doi.org/10.1006/jmaa.1993.1324.

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21

Arrieta, José M., Rosa Pardo, and Anibal Rodríguez-Bernal. "Bifurcation and stability of equilibria with asymptotically linear boundary conditions at infinity." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 137, no. 2 (2007): 225–52. http://dx.doi.org/10.1017/s0308210505000363.

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We consider an elliptic equation with a nonlinear boundary condition which is asymptotically linear at infinity and which depends on a parameter. As the parameter crosses some critical values, there appear certain resonances in the equation producing solutions that bifurcate from infinity. We study the bifurcation branches, characterize when they are sub- or supercritical and analyse the stability type of the solutions. Furthermore, we apply these results and techniques to obtain Landesman–Lazer-type conditions guaranteeing the existence of solutions in the resonant case and to obtain an anti-maximum principle.
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22

Gezahegn, Natnael, and Tadesse Abdi. "Spectral problem for the Laplacian and a selfadjoint nonlinear elliptic boundary value problem." SINET: Ethiopian Journal of Science 45, no. 2 (August 30, 2022): 224–34. http://dx.doi.org/10.4314/sinet.v45i2.8.

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In this paper, we present some connections between the spectral problem, −Δu(x) = λ1u(x) in Ω,u(x) = 0 on ∂Ω and selfadjoint boundary value problem, Δu(x) − λ1u(x) + g(x, u(x)) = h(x) in Ω,u(x) = 0 on ∂Ω, where λ1 is the smallest eigenvalue of −∆, Ω ⊆ Rn is a bounded domain, h ∈ L2(Ω) and the nonlinear function g is a Caratheodory function satisfying a growth condition. We initially investigate the existence of solutions for the spectral problem by considering the selfadjoint boundary value problem. The selfadjoint boundary value problem is then considered for both existence and estimation results. We use degree argument in order to show that the selfadjoint boundary value problem has a solution instead of the Landesman-Lazer condition or the monotonocity assumption on the second argument of the function g. In this paper, we present some connections between the spectral problem, and selfadjoint boundary value problem, where λ1 is the smallest eigenvalue of −∆, Ω ⊆ Rn is a bounded domain, h ∈ L2(Ω) and the nonlinear function g is a Caratheodory function satisfying a growth condition. We initially investigate the existence of solutions for the spectral problem by considering the selfadjoint boundary value problem. The selfadjoint boundary value problem is then considered for both existence and estimation results. We use degree argument in order to show that the selfadjoint boundary value problem has a solution instead of the Landesman-Lazer condition or the monotonocity assumption on the second argument of the function g.
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23

Kuo, Chung-Cheng. "On the Solvability of a Neumann Boundary Value Problem at Resonance." Canadian Mathematical Bulletin 40, no. 4 (December 1, 1997): 464–70. http://dx.doi.org/10.4153/cmb-1997-055-7.

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AbstractWe study the existence of solutions of the semilinear equations (1) in which the non-linearity g may grow superlinearly in u in one of directions u → ∞ and u → −∞, and (2) −Δu + g(x, u) = h, in which the nonlinear term g may grow superlinearly in u as |u| → ∞. The purpose of this paper is to obtain solvability theorems for (1) and (2) when the Landesman-Lazer condition does not hold. More precisely, we require that h may satisfy are arbitrarily nonnegative constants, . The proofs are based upon degree theoretic arguments.
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24

Li, Jin, and Zaihong Wang. "A Landesman-Lazer type condition for second-order differential equations with a singularity at resonance." Complex Variables and Elliptic Equations 60, no. 5 (October 2014): 620–34. http://dx.doi.org/10.1080/17476933.2014.964228.

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25

Yeh, Nai-Sher. "On Solvability Theorems of Second-Order Ordinary Differential Equations with Delay." Abstract and Applied Analysis 2018 (2018): 1–6. http://dx.doi.org/10.1155/2018/5321314.

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For eachx0∈[0,2π)andk∈N, we obtain some existence theorems of periodic solutions to the two-point boundary value problemu′′(x)+k2u(x-x0)+g(x,u(x-x0))=h(x)in(0,2π)withu(0)-u(2π)=u′(0)-u′(2π)=0wheng:(0,2π)×R→Ris a Caratheodory function which grows linearly inuasu→∞, andh∈L1(0,2π)may satisfy a generalized Landesman-Lazer condition(1+sign(β))∫02πh(x)v(x)dx<∫v(x)>0gβ+(x)vx1-βdx+∫v(x)<0gβ-(x)vx1-βdxfor allv∈N(L)\{0}. HereN(L)denotes the subspace ofL1(0,2π)spanned bysin⁡kxandcos⁡kx,-1<β≤0,gβ+(x)=lim infu→∞(gx,uu/u1-β), andgβ-(x)=lim infu→-∞(gx,uu/u1-β).
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26

Deng, Yinbin, Wentao Huang, and Shen Zhang. "Ground State Solutions for Quasilinear Schrödinger Equations with Critical Growth and Lower Power Subcritical Perturbation." Advanced Nonlinear Studies 19, no. 1 (February 1, 2019): 219–37. http://dx.doi.org/10.1515/ans-2018-2029.

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Abstract We study the following generalized quasilinear Schrödinger equation: -(g^{2}(u)\nabla u)+g(u)g^{\prime}(u)|\nabla u|^{2}+V(x)u=h(u),\quad x\in% \mathbb{R}^{N}, where {N\geq 3} , {g\colon\mathbb{R}\rightarrow\mathbb{R}^{+}} is an even differentiable function such that {g^{\prime}(t)\geq 0} for all {t\geq 0} , {h\in C^{1}(\mathbb{R},\mathbb{R})} is a nonlinear function including critical growth and lower power subcritical perturbation, and the potential {V(x)\colon\mathbb{R}^{N}\rightarrow\mathbb{R}} is positive. Since the subcritical perturbation does not satisfy the (AR) condition, the standard variational method cannot be used directly. Combining the change of variables and the monotone method developed by Jeanjean in [L. Jeanjean, On the existence of bounded Palais–Smale sequences and application to a Landesman–Lazer-type problem set on {\mathbf{R}}^{N} , Proc. Roy. Soc. Edinburgh Sect. A 129 1999, 4, 787–809], we obtain the existence of positive ground state solutions for the given problem.
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27

Arcoya, David, and Luigi Orsina. "Landesman-lazer conditions and quasilinear elliptic equations." Nonlinear Analysis: Theory, Methods & Applications 28, no. 10 (May 1997): 1623–32. http://dx.doi.org/10.1016/s0362-546x(96)00022-3.

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28

Volek, Jonáš. "Landesman–Lazer conditions for difference equations involving sublinear perturbations." Journal of Difference Equations and Applications 22, no. 11 (September 19, 2016): 1698–719. http://dx.doi.org/10.1080/10236198.2016.1234617.

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29

da Silva, Edcarlos D. "Multiplicity of Solutions for Gradient Systems Using Landesman-Lazer Conditions." Abstract and Applied Analysis 2010 (2010): 1–22. http://dx.doi.org/10.1155/2010/237826.

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We establish existence and multiplicity of solutions for an elliptic system which presents resonance at infinity of Landesman-Lazer type. In order to describe the resonance, we use an eigenvalue problem with indefinite weights. In all results, we use Variational Methods, Morse Theory and Critical Groups.
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30

Amster, Pablo. "On Landesman-Lazer conditions and the fundamental theorem of algebra." Monatshefte für Mathematik 195, no. 3 (April 3, 2021): 381–89. http://dx.doi.org/10.1007/s00605-021-01553-5.

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31

Genoud, François, and Bryan P. Rynne. "Landesman–Lazer conditions at half-eigenvalues of the p -Laplacian." Journal of Differential Equations 254, no. 8 (April 2013): 3461–75. http://dx.doi.org/10.1016/j.jde.2013.01.029.

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32

Kannan, R., and R. Ortega. "Landesman-Lazer conditions for problems with “one- side unbounded” nonlinearities." Nonlinear Analysis: Theory, Methods & Applications 9, no. 12 (January 1985): 1313–17. http://dx.doi.org/10.1016/0362-546x(85)90090-2.

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33

Amster, Pablo. "Nagumo and Landesman-Lazer type conditions for nonlinear second order systems." Nonlinear Differential Equations and Applications NoDEA 13, no. 5-6 (July 2007): 699–711. http://dx.doi.org/10.1007/s00030-006-4042-8.

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34

Rynne, Bryan P. "Landesman–Lazer conditions for resonant p-Laplacian problems with jumping nonlinearities." Journal of Differential Equations 261, no. 10 (November 2016): 5829–43. http://dx.doi.org/10.1016/j.jde.2016.08.021.

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35

Fabry, C. "Landesman-Lazer Conditions for Periodic Boundary Value Problems with Asymmetric Nonlinearities." Journal of Differential Equations 116, no. 2 (March 1995): 405–18. http://dx.doi.org/10.1006/jdeq.1995.1040.

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36

Mavinga, Nsoki, and Rosa Pardo. "Bifurcation from infinity for reaction–diffusion equations under nonlinear boundary conditions." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 147, no. 3 (March 20, 2017): 649–71. http://dx.doi.org/10.1017/s0308210516000251.

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We consider reaction–diffusion equations under nonlinear boundary conditions where the nonlinearities are asymptotically linear at infinity and depend on a parameter. We prove that, as the parameter crosses some critical values, a resonance-type phenomenon provides solutions that bifurcate from infinity. We characterize the bifurcated branches when they are sub- or supercritical. We obtain both Landesman–Lazer-type conditions that guarantee the existence of solutions in the resonant case and an anti-maximum principle.
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37

Le, Vy Khoi. "On some noncoercive variational inequalities containing degenerate elliptic operators." ANZIAM Journal 44, no. 3 (January 2003): 409–30. http://dx.doi.org/10.1017/s1446181100008117.

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AbstractWe are concerned with the solvability of variational inequalities that contain degenerate elliptic operators. By using a recession approach, we find conditions on the boundary conditions such that the inequality has at least one solution. Existence results of Landesman-Lazer type for a nonsmooth inequality and a resonance problem for a weighted p-Laplacian are discussed in detail.
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38

Amster, Pablo, and Pablo De Nápoli. "Landesman–Lazer type conditions for a system of p-Laplacian like operators." Journal of Mathematical Analysis and Applications 326, no. 2 (February 2007): 1236–43. http://dx.doi.org/10.1016/j.jmaa.2006.04.001.

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39

Amster, Pablo. "Non-asymptotic and potential Landesman-Lazer conditions for a nonlinear beam equation." Journal of Applied Mathematics and Computing 40, no. 1-2 (March 28, 2012): 63–72. http://dx.doi.org/10.1007/s12190-012-0552-1.

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40

ORTEGA, RAFAEL, and LUIS A. SÁNCHEZ. "PERIODIC SOLUTIONS OF FORCED OSCILLATORS WITH SEVERAL DEGREES OF FREEDOM." Bulletin of the London Mathematical Society 34, no. 3 (May 2002): 308–18. http://dx.doi.org/10.1112/s0024609301008748.

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Results of the Landesman–Lazer type provide necessary and sufficient conditions for the existence of periodic solutions of certain nonlinear differential equations with forcing. Typically, they deal with scalar problems. This paper presents a discussion of possible extensions to systems. The emphasis is placed on the new phenomena produced by the increase of the dimension.
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41

Gasiński, Leszek, and Nikolaos S. Papageorgiou. "Solutions and multiple solutions for quasilinear hemivariational inequalities at resonance." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 131, no. 5 (October 2001): 1091–111. http://dx.doi.org/10.1017/s0308210500001281.

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In this paper we consider quasilinear hemivariational inequalities at resonance. We obtain existence theorems using Landesman-Lazer-type conditions and multiplicity theorems for problems with strong resonance at infinity. Our method of proof is based on the non-smooth critical point theory for locally Lipschitz functions and on a generalized version of the Ekeland variational principle.
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42

Fonda, Alessandro, and Maurizio Garrione. "Double resonance with Landesman–Lazer conditions for planar systems of ordinary differential equations." Journal of Differential Equations 250, no. 2 (January 2011): 1052–82. http://dx.doi.org/10.1016/j.jde.2010.08.006.

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43

Fonda, Alessandro, and Rodica Toader. "Subharmonic solutions of Hamiltonian systems displaying some kind of sublinear growth." Advances in Nonlinear Analysis 8, no. 1 (July 28, 2017): 583–602. http://dx.doi.org/10.1515/anona-2017-0040.

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Abstract We prove the existence and multiplicity of subharmonic solutions for Hamiltonian systems obtained as perturbations of N planar uncoupled systems which, e.g., model some type of asymmetric oscillators. The nonlinearities are assumed to satisfy Landesman–Lazer conditions at the zero eigenvalue, and to have some kind of sublinear behavior at infinity. The proof is carried out by the use of a generalized version of the Poincaré–Birkhoff Theorem. Different situations, including Lotka–Volterra systems, or systems with singularities, are also illustrated.
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44

Da Silva, Edcarlos Domingos, and Francisco Odair De Paiva. "Landesman-lazer type conditions and multiplicity results for nonlinear elliptic problems with neumann boundary values." Acta Mathematica Sinica, English Series 30, no. 2 (January 15, 2014): 229–50. http://dx.doi.org/10.1007/s10114-014-2750-2.

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45

Gal, Ciprian G., and Mahamadi Warma. "Nonlinear Elliptic Boundary Value Problems at Resonance with Nonlinear Wentzell Boundary Conditions." Advances in Mathematical Physics 2017 (2017): 1–20. http://dx.doi.org/10.1155/2017/5196513.

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Given a bounded domain Ω⊂RN with a Lipschitz boundary ∂Ω and p,q∈(1,+∞), we consider the quasilinear elliptic equation -Δpu+α1u=f in Ω complemented with the generalized Wentzell-Robin type boundary conditions of the form bx∇up-2∂nu-ρbxΔq,Γu+α2u=g on ∂Ω. In the first part of the article, we give necessary and sufficient conditions in terms of the given functions f, g and the nonlinearities α1, α2, for the solvability of the above nonlinear elliptic boundary value problems with the nonlinear boundary conditions. In other words, we establish a sort of “nonlinear Fredholm alternative” for our problem which extends the corresponding Landesman and Lazer result for elliptic problems with linear homogeneous boundary conditions. In the second part, we give some additional results on existence and uniqueness and we study the regularity of the weak solutions for these classes of nonlinear problems. More precisely, we show some global a priori estimates for these weak solutions in an L∞-setting.
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46

Ayazoglu- Sidika S¸ ule S¸ ener · Tuba Agırman Aydın, Rabil. "Existence of solutions for a resonant problem under Landesman-Lazer type conditions involving more general elliptic operators in divergence form." Proceedings of the Institute of Mathematics and Mechanics,National Academy of Sciences of Azerbaijan 1, no. 1 (2020): 52–65. http://dx.doi.org/10.29228/proc.62.

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47

Ayazoglu- Sidika S¸ ule S¸ ener · Tuba Agırman Aydın, Rabil. "Existence of solutions for a resonant problem under Landesman-Lazer type conditions involving more general elliptic operators in divergence form." Proceedings of the Institute of Mathematics and Mechanics,National Academy of Sciences of Azerbaijan 1, no. 1 (2020): 52–65. http://dx.doi.org/10.29228/proc.63.

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48

Arcoya, D., M. C. M. Rezende, and E. A. B. Silva. "Quasilinear problems under local Landesman–Lazer condition." Calculus of Variations and Partial Differential Equations 58, no. 6 (November 13, 2019). http://dx.doi.org/10.1007/s00526-019-1650-9.

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49

Fonda, Alessandro, and Maurizio Garrione. "Nonlinear Resonance: a Comparison Between Landesman-Lazer and Ahmad-Lazer-Paul Conditions." Advanced Nonlinear Studies 11, no. 2 (January 1, 2011). http://dx.doi.org/10.1515/ans-2011-0209.

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AbstractWe show that the Ahmad-Lazer-Paul condition for resonant problems is more general than the Landesman-Lazer one, discussing some relations with other existence conditions, as well. As a consequence, such a relation holds, for example, when considering resonant boundary value problems associated with linear elliptic operators, the p-Laplacian and, in the scalar case, with an asymmetric oscillator.
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50

Sfecci, Andrea. "Periodic Impact Motions at Resonance of a Particle Bouncing on Spheres and Cylinders." Advanced Nonlinear Studies 17, no. 3 (January 1, 2017). http://dx.doi.org/10.1515/ans-2016-6026.

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AbstractWe investigate the existence of periodic trajectories of a particle, subject to a central force, which can hit a sphere or a cylinder. We will also provide a Landesman–Lazer-type condition in the case of a nonlinearity satisfying a
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