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Relevant bibliographies by topics / (p,q)-Laplacian

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Journal articles

Academic literature on the topic '(p,q)-Laplacian'

Author: Grafiati

Published: 10 March 2023

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Journal articles on the topic "(p,q)-Laplacian"

1

Hsu, Tsing-San, and Huei-Li Lin. "Multiplicity of Positive Solutions for ap-q-Laplacian Type Equation with Critical Nonlinearities." Abstract and Applied Analysis 2014 (2014): 1–9. http://dx.doi.org/10.1155/2014/829069.

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We study the effect of the coefficientf(x)of the critical nonlinearity on the number of positive solutions for ap-q-Laplacian equation. Under suitable assumptions forf(x)andg(x), we should prove that for sufficiently smallλ>0, there exist at leastkpositive solutions of the followingp-q-Laplacian equation,-Δpu-Δqu=fxu|p*-2u+λgxu|r-2u in Ω,u=0 on ∂Ω,whereΩ⊂RNis a bounded smooth domain,N>p,1<q<N(p-1)/(N-1)<p≤max⁡{p,p^*-q/(p-1)}<r<p^*,p^*=Np/(N-p)is the critical Sobolev exponent, andΔsu=div(|∇u|s-2∇uis thes-Laplacian ofu.

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2

Motreanu, Dumitru. "Quasilinear Dirichlet problems with competing operators and convection." Open Mathematics 18, no. 1 (2020): 1510–17. http://dx.doi.org/10.1515/math-2020-0112.

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Abstract The paper deals with a quasilinear Dirichlet problem involving a competing (p,q)-Laplacian and a convection term. Due to the lack of ellipticity, monotonicity and variational structure, the known methods to find a weak solution are not applicable. We develop an approximation procedure permitting to establish the existence of solutions in a generalized sense. If in place of competing (p,q)-Laplacian we consider the usual (p,q)-Laplacian, our results ensure the existence of weak solutions.

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3

Motreanu, Dumitru. "Quasilinear Dirichlet problems with competing operators and convection." Open Mathematics 18, no. 1 (2020): 1510–17. http://dx.doi.org/10.1515/math-2020-0112.

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Abstract The paper deals with a quasilinear Dirichlet problem involving a competing (p,q)-Laplacian and a convection term. Due to the lack of ellipticity, monotonicity and variational structure, the known methods to find a weak solution are not applicable. We develop an approximation procedure permitting to establish the existence of solutions in a generalized sense. If in place of competing (p,q)-Laplacian we consider the usual (p,q)-Laplacian, our results ensure the existence of weak solutions.

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4

Abolarinwa, Abimbola, and Shahroud Azami. "Comparison estimates on the first eigenvalue of a quasilinear elliptic system." Journal of Applied Analysis 26, no. 2 (2020): 273–85. http://dx.doi.org/10.1515/jaa-2020-2024.

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AbstractWe study a system of quasilinear eigenvalue problems with Dirichlet boundary conditions on complete compact Riemannian manifolds. In particular, Cheng comparison estimates and the inequality of Faber–Krahn for the first eigenvalue of a {(p,q)}-Laplacian are recovered. Lastly, we reprove a Cheeger-type estimate for the p-Laplacian, {1<p<\infty}, from where a lower bound estimate in terms of Cheeger’s constant for the first eigenvalue of a {(p,q)}-Laplacian is built. As a corollary, the first eigenvalue converges to Cheeger’s constant as {p,q\to 1,1}.

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5

Gasiński, Leszek, and Nikolaos S. Papageorgiou. "Resonant Anisotropic (p,q)-Equations." Mathematics 8, no. 8 (2020): 1332. http://dx.doi.org/10.3390/math8081332.

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We consider an anisotropic Dirichlet problem which is driven by the (p(z),q(z))-Laplacian (that is, the sum of a p(z)-Laplacian and a q(z)-Laplacian), The reaction (source) term, is a Carathéodory function which asymptotically as x±∞ can be resonant with respect to the principal eigenvalue of (−Δp(z),W01,p(z)(Ω)). First using truncation techniques and the direct method of the calculus of variations, we produce two smooth solutions of constant sign. In fact we show that there exist a smallest positive solution and a biggest negative solution. Then by combining variational tools, with suitable truncation techniques and the theory of critical groups, we show the existence of a nodal (sign changing) solution, located between the two extremal ones.

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6

李, 燕茹. "On a Class of (p(u),q(u))-Laplacian Problem." Pure Mathematics 11, no. 04 (2021): 586–98. http://dx.doi.org/10.12677/pm.2021.114072.

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7

Papageorgiou, Nikolaos S., Dongdong Qin, and Vicenţiu D. Rădulescu. "Nonlinear eigenvalue problems for the (p,q)–Laplacian." Bulletin des Sciences Mathématiques 172 (November 2021): 103039. http://dx.doi.org/10.1016/j.bulsci.2021.103039.

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8

Haghaiegh, Somayeh, and Ghasem Afrouzi. "Sub-super solutions for (p-q) Laplacian systems." Boundary Value Problems 2011, no. 1 (2011): 52. http://dx.doi.org/10.1186/1687-2770-2011-52.

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9

Manouni, Said El, Kanishka Perera, and Ratnasingham Shivaji. "On singular quasi-monotone (p, q)-Laplacian systems." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 142, no. 3 (2012): 585–94. http://dx.doi.org/10.1017/s0308210510001356.

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10

Humphries, Peter. "Spectral Multiplicity for Maaß Newforms of Non-Squarefree Level." International Mathematics Research Notices 2019, no. 18 (2017): 5703–43. http://dx.doi.org/10.1093/imrn/rnx283.

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Abstract We show that if a positive integer $q$ has $s(q)$ odd prime divisors $p$ for which $p^2$ divides $q$, then a positive proportion of the Laplacian eigenvalues of Maaß newforms of weight $0$, level $q$, and principal character occur with multiplicity at least $2^{s(q)}$. Consequently, the new part of the cuspidal spectrum of the Laplacian on $\Gamma_0(q) \backslash \mathbb{H}$ cannot be simple for any odd non-squarefree integer $q$. This generalises work of Strömberg who proved this for $q = 9$ by different methods.

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