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Journal articles on the topic 'Unbounded Coefficients'

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Published: 9 March 2023
Last updated: 11 March 2023

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1

Da Prato, G., and A. Ichikawa. "Riccati equations with unbounded coefficients." Annali di Matematica Pura ed Applicata 140, no. 1 (December 1985): 209–21. http://dx.doi.org/10.1007/bf01776850.

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2

Greco, Luigi, Gioconda Moscariello, and Teresa Radice. "Nondivergence elliptic equations with unbounded coefficients." Discrete & Continuous Dynamical Systems - B 11, no. 1 (2009): 131–43. http://dx.doi.org/10.3934/dcdsb.2009.11.131.

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3

Latushkin, Yuri, and Yuri Tomilov. "Fredholm differential operators with unbounded coefficients." Journal of Differential Equations 208, no. 2 (January 2005): 388–429. http://dx.doi.org/10.1016/j.jde.2003.10.018.

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4

Kudlak, Zachary, and R. Patrick Vernon. "Unbounded rational systems with nonconstant coefficients." Nonautonomous Dynamical Systems 9, no. 1 (January 1, 2022): 307–16. http://dx.doi.org/10.1515/msds-2022-0160.

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Abstract We show the existence of unbounded solutions to difference equations of the form { x n + 1 = c ′ n x n B n y n , y n + 1 = b n x n + c n y n A n + C n y n f o r n = 0 , 1 , … , \left\{ {\matrix{{{x_{n + 1}} = {{{{c'}_n}{x_n}} \over {{B_n}{y_n}}},} \hfill \cr {{y_{n + 1}} = {{{b_n}{x_n} + {c_n}{y_n}} \over {{A_n} + {C_n}{y_n}}}} \hfill \cr } \,\,\,\,\,for} \right.\,\,\,n = 0,1, \ldots , where { c ′ n } n = 0 ∞ \left\{ {{{c'}_n}} \right\}_{n = 0}^\infty , { B ′ n } n = 0 ∞ \left\{ {{{B'}_n}} \right\}_{n = 0}^\infty , { b n } n = 0 ∞ \left\{ {{b_n}} \right\}_{n = 0}^\infty , { c n } n = 0 ∞ \left\{ {{c_n}} \right\}_{n = 0}^\infty , and { A n } n = 0 ∞ \left\{ {{A_n}} \right\}_{n = 0}^\infty are all bounded above and below by positive constants, and { C n } n = 0 ∞ \left\{ {{C_n}} \right\}_{n = 0}^\infty is either bounded above and below by positive constants or is identically zero. In the latter case, we give an example which can be reduced to a system of the form { x n + 1 = x n y n , y n + 1 = x n + γ n y n f o r n = 0 , 1 , … , \left\{ {\matrix{ {{x_{n + 1}} = {{{x_n}} \over {{y_n}}},} \hfill \cr {{y_{n + 1}} = {x_n} + {\gamma _n}{y_n}} \hfill \cr } \,\,\,\,\,for} \right.\,\,\,n = 0,1, \ldots , where 0 < γ′ < γ n < γ < 1 for some constants γ and γ′ for all n. This provides a counterexample to the main result of the 2021 paper by Camouzis and Kotsios.
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5

Kusano, Takaŝi, and Marko Švec. "On unbounded positive solutions of nonlinear differential equations with oscillating coefficients." Czechoslovak Mathematical Journal 39, no. 1 (1989): 133–41. http://dx.doi.org/10.21136/cmj.1989.102285.

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6

Czornik, Adam, and Michał Niezabitowski. "Lyapunov exponents for systems with unbounded coefficients." Dynamical Systems 28, no. 2 (June 2013): 140–53. http://dx.doi.org/10.1080/14689367.2012.742038.

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7

Kunze, Markus, Luca Lorenzi, and Alessandra Lunardi. "Nonautonomous Kolmogorov parabolic equations with unbounded coefficients." Transactions of the American Mathematical Society 362, no. 01 (August 3, 2009): 169–98. http://dx.doi.org/10.1090/s0002-9947-09-04738-2.

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8

Lorenzi, Luca, and Alessandro Zamboni. "Cores for parabolic operators with unbounded coefficients." Journal of Differential Equations 246, no. 7 (April 2009): 2724–61. http://dx.doi.org/10.1016/j.jde.2008.12.015.

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9

Zalygina, V. I. "Lyapunov Equivalence of Systems with Unbounded Coefficients." Journal of Mathematical Sciences 210, no. 2 (September 5, 2015): 210–16. http://dx.doi.org/10.1007/s10958-015-2558-3.

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10

Cicognani, Massimo. "Coefficients with unbounded derivatives in hyperbolic equations." Mathematische Nachrichten 276, no. 1 (October 2004): 31–46. http://dx.doi.org/10.1002/mana.200310210.

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11

Da Prato, Giuseppe, and Beniamin Goldys. "Elliptic Operators on Rd with Unbounded Coefficients." Journal of Differential Equations 172, no. 2 (May 2001): 333–58. http://dx.doi.org/10.1006/jdeq.2000.3866.

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12

Gashi, Bujar, and Jiajie Li. "Integrability of exponential process and its application to backward stochastic differential equations." IMA Journal of Management Mathematics 30, no. 4 (June 21, 2018): 335–65. http://dx.doi.org/10.1093/imaman/dpy008.

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Abstract We consider the integrability problem of an exponential process with unbounded coefficients. The integrability is established under weaker conditions of Kazamaki type, which complements the results of Yong obtained under a Novikov type condition. As applications, we consider the solvability of linear backward stochastic differential equations (BSDEs) and market completeness, the solvability of a Riccati BSDE and optimal investment, all in the setting of unbounded coefficients.
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13

Dong, Wei, and Yihong Du. "Unbounded principal eigenfunctions and the logistic equation on RN." Bulletin of the Australian Mathematical Society 67, no. 3 (June 2003): 413–27. http://dx.doi.org/10.1017/s0004972700037229.

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We consider the logistic equation − Δu = a (x) u − b (x) up on all of RN with possibly unbounded coefficients near infinity. We show that under suitable growth conditions of the coefficients, the behaviour of the positive solutions of the logistic equation can be largely determined. We also show that certain linear eigenvalue problems on all of RN have principal eigenfunctions that become unbounded near infinity at an exponential rate. Using these results, we finally show that the logistic equation has a unique positive solution under suitable growth restrictions for its coefficients.
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14

Bertoldi, M., and S. Fornaro. "Gradient estimates in parabolic problems with unbounded coefficients." Studia Mathematica 165, no. 3 (2004): 221–54. http://dx.doi.org/10.4064/sm165-3-3.

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15

Florchinger, Patrick, and Giovanna Nappo. "Continuity of the Filter with Unbounded Observation Coefficients." Stochastic Analysis and Applications 29, no. 4 (July 2011): 612–30. http://dx.doi.org/10.1080/07362994.2011.581087.

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16

Czornik, Adam, and Michal Niezabitowski. "Corrigendum Lyapunov exponents for systems with unbounded coefficients." Dynamical Systems 28, no. 2 (June 2013): 299. http://dx.doi.org/10.1080/14689367.2012.756700.

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17

Fagnola, Franco, and Stephen J. Wills. "Solving quantum stochastic differential equations with unbounded coefficients." Journal of Functional Analysis 198, no. 2 (March 2003): 279–310. http://dx.doi.org/10.1016/s0022-1236(02)00089-7.

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18

Aptekarev, A. I., and J. S. Geronimo. "Measures for orthogonal polynomials with unbounded recurrence coefficients." Journal of Approximation Theory 207 (July 2016): 339–47. http://dx.doi.org/10.1016/j.jat.2016.02.009.

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19

Filinovskii, A. V. "Hyperbolic Equations with Growing Coefficients in Unbounded Domains." Journal of Mathematical Sciences 197, no. 3 (February 5, 2014): 435–46. http://dx.doi.org/10.1007/s10958-014-1725-2.

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20

Shiryaev, K. E. "Central Exponent of a System with Unbounded Coefficients." Journal of Mathematical Sciences 210, no. 3 (September 24, 2015): 331–32. http://dx.doi.org/10.1007/s10958-015-2568-1.

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21

Gy�ngy, Istv�n, and Nicolai V. Krylov. "On stochastic partial differential equations with Unbounded coefficients." Potential Analysis 1, no. 3 (September 1992): 233–56. http://dx.doi.org/10.1007/bf00269509.

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22

Metafune, Giorgio, and Chiara Spina. "A degenerate elliptic operator with unbounded diffusion coefficients." Rendiconti Lincei - Matematica e Applicazioni 25, no. 2 (2014): 109–40. http://dx.doi.org/10.4171/rlm/670.

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23

Angiuli, Luciana, and Luca Lorenzi. "On coupled systems of PDEs with unbounded coefficients." Dynamics of Partial Differential Equations 17, no. 2 (2020): 129–63. http://dx.doi.org/10.4310/dpde.2020.v17.n2.a3.

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24

Escauriaza, Luis, and Steve Hofmann. "Kato square root problem with unbounded leading coefficients." Proceedings of the American Mathematical Society 146, no. 12 (September 17, 2018): 5295–310. http://dx.doi.org/10.1090/proc/14224.

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25

Fagnola, Franco. "On quantum stochastic differential equations with unbounded coefficients." Probability Theory and Related Fields 86, no. 4 (December 1990): 501–16. http://dx.doi.org/10.1007/bf01198172.

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26

Bayandiyev, Ye N. "About the Storm-Liouville operator with negative parameter in space L2(R)." Bulletin of the National Engineering Academy of the Republic of Kazakhstan 80, no. 2 (June 30, 2021): 34–40. http://dx.doi.org/10.47533/2020.1606-146x.82.

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In this paper, the question of the existence of a resolvent is studied, and also, after closure in space, the smoothness of functions from the domain of an operator of the unbounded type in an unbounded domain with coefficients strongly increasing at infinity is investigated.
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27

Muratbekov, Mussakan, and Yerik Bayandiyev. "On the resolvent existence and the separability of a hyperbolic operator with fast growing coefficients in L2(R2)." Filomat 35, no. 3 (2021): 707–21. http://dx.doi.org/10.2298/fil2103707m.

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This paper studies the question of the resolvent existence, as well as, the smoothness of elements from the definition domain (separability) of a class of hyperbolic differential operators defined in an unbounded domain with greatly increasing coefficients after a closure in the space L2(R2). Such a problem was previously put forward by I.M. Gelfand for elliptic operators. Here, we note that a detailed analysis shows that when studying the spectral properties of differential operators specified in an unbounded domain, the behavior of the coefficients at infinity plays an important role.
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28

Chicco, Maurizio, and Marina Venturino. "Dirichlet problem for a divergence form elliptic equation with unbounded coefficients in an unbounded domain." Annali di Matematica Pura ed Applicata 178, no. 1 (December 2000): 325–38. http://dx.doi.org/10.1007/bf02505902.

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29

Baskakov, A. G., and V. B. Didenko. "Spectral analysis of differential operators with unbounded periodic coefficients." Differential Equations 51, no. 3 (March 2015): 325–41. http://dx.doi.org/10.1134/s0012266115030052.

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30

Cherepova, M. F. "The Cauchy problem for parabolic equations with unbounded coefficients." Doklady Mathematics 91, no. 3 (May 2015): 364–66. http://dx.doi.org/10.1134/s1064562415030254.

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31

Vlasov, V. V., and N. A. Rautian. "Study of functional-differential equations with unbounded operator coefficients." Doklady Mathematics 96, no. 3 (November 2017): 620–24. http://dx.doi.org/10.1134/s1064562417060291.

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32

Manca, Luigi. "Fokker–Planck Equation for Kolmogorov Operators with Unbounded Coefficients." Stochastic Analysis and Applications 27, no. 4 (June 22, 2009): 747–69. http://dx.doi.org/10.1080/07362990902976579.

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33

Da Prato, Giuseppe, and Vincenzo Vespri. "Maximal Lp regularity for elliptic equations with unbounded coefficients." Nonlinear Analysis: Theory, Methods & Applications 49, no. 6 (June 2002): 747–55. http://dx.doi.org/10.1016/s0362-546x(01)00133-x.

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34

Della Pietra, Francesco, and Giuseppina di Blasio. "Existence results for nonlinear elliptic problems with unbounded coefficients." Nonlinear Analysis: Theory, Methods & Applications 71, no. 1-2 (July 2009): 72–87. http://dx.doi.org/10.1016/j.na.2008.10.047.

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35

Castro Santis, Ricardo, and Alberto Barchielli. "Quantum stochastic differential equations and continuous measurements: unbounded coefficients." Reports on Mathematical Physics 67, no. 2 (April 2011): 229–54. http://dx.doi.org/10.1016/s0034-4877(11)80014-5.

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36

Monsurrò, Sara, and Maria Transirico. "Noncoercive elliptic equations with discontinuous coefficients in unbounded domains." Nonlinear Analysis 163 (November 2017): 86–103. http://dx.doi.org/10.1016/j.na.2017.07.008.

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37

Candela, A. M., and A. Salvatore. "Normal geodesics in stationary Lorentzian manifolds with unbounded coefficients." Journal of Geometry and Physics 44, no. 2-3 (December 2002): 171–95. http://dx.doi.org/10.1016/s0393-0440(02)00060-8.

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38

Geronimo, Jeffrey S., and Walter Van Assche. "Relative asymptotics for orthogonal polynomials with unbounded recurrence coefficients." Journal of Approximation Theory 62, no. 1 (July 1990): 47–69. http://dx.doi.org/10.1016/0021-9045(90)90046-s.

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39

Assing, Sigurd, and Ralf Manthey. "Invariant measures for stochastic heat equations with unbounded coefficients." Stochastic Processes and their Applications 103, no. 2 (February 2003): 237–56. http://dx.doi.org/10.1016/s0304-4149(02)00211-9.

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40

Zhang, Xicheng. "Stochastic partial differential equations with unbounded and degenerate coefficients." Journal of Differential Equations 250, no. 4 (February 2011): 1924–66. http://dx.doi.org/10.1016/j.jde.2010.11.021.

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41

Chebotarev, A. M., J. C. Garcia, and R. B. Quezada. "On the lindblad equation with unbounded time-dependent coefficients." Mathematical Notes 61, no. 1 (January 1997): 105–17. http://dx.doi.org/10.1007/bf02355012.

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42

Böttcher, Björn. "On the construction of Feller processes with unbounded coefficients." Electronic Communications in Probability 16 (2011): 545–55. http://dx.doi.org/10.1214/ecp.v16-1652.

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43

Murtazin, Kh Kh, and A. N. Galimov. "Spectrum and scattering for Schrödinger operators with unbounded coefficients." Doklady Mathematics 73, no. 2 (June 2006): 223–25. http://dx.doi.org/10.1134/s1064562406020190.

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44

Bichegkuev, M. S. "Lyapunov transformation of differential operators with unbounded operator coefficients." Mathematical Notes 99, no. 1-2 (January 2016): 24–36. http://dx.doi.org/10.1134/s000143461601003x.

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45

Karrmann, Stefan. "Gaussian Estimates for Second-Order Operators with Unbounded Coefficients." Journal of Mathematical Analysis and Applications 258, no. 1 (June 2001): 320–48. http://dx.doi.org/10.1006/jmaa.2001.7507.

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46

Ramm, A. G. "Uniqueness theorems for multidimensional inverse problems with unbounded coefficients." Journal of Mathematical Analysis and Applications 136, no. 2 (December 1988): 568–74. http://dx.doi.org/10.1016/0022-247x(88)90105-9.

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47

Kumar, M. Sathish, R. Elayaraja, V. Ganesan, Omar Bazighifan, Khalifa Al-Shaqsi, and Kamsing Nonlaopon. "Qualitative Behavior of Unbounded Solutions of Neutral Differential Equations of Third-Order." Fractal and Fractional 5, no. 3 (August 12, 2021): 95. http://dx.doi.org/10.3390/fractalfract5030095.

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New oscillatory properties for the oscillation of unbounded solutions to a class of third-order neutral differential equations with several deviating arguments are established. Several oscillation results are established by using generalized Riccati transformation and a integral average technique under the case of unbounded neutral coefficients. Examples are given to prove the significance of new theorems.
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48

Branquinho, Amílcar, Juan Garca-Ardila, and Francisco Marcellán. "Ratio asymptotics for biorthogonal matrix polynomials with unbounded recurrence coefficients." Applicable Analysis and Discrete Mathematics, no. 00 (2020): 51. http://dx.doi.org/10.2298/aadm190225051b.

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In this paper we study matrix biorthogonal polynomials sequences that satisfy a nonsymmetric three term recurrence relation with unbounded matrix coefficients. The outer ratio asymptotics for this family of matrix biorthogonal polynomials is derived under quite general assumptions. Some illustrative examples are considered.
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49

Fornaro, Simona, Nicola Fusco, Giorgio Metafune, and Diego Pallara. "Sharp upper bounds for the density of some invariant measures." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 139, no. 6 (November 4, 2009): 1145–61. http://dx.doi.org/10.1017/s0308210508000498.

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50

Kian, Yavar. "RECOVERY OF NON-COMPACTLY SUPPORTED COEFFICIENTS OF ELLIPTIC EQUATIONS ON AN INFINITE WAVEGUIDE." Journal of the Institute of Mathematics of Jussieu 19, no. 5 (November 5, 2018): 1573–600. http://dx.doi.org/10.1017/s1474748018000488.

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We consider the unique recovery of a non-compactly supported and non-periodic perturbation of a Schrödinger operator in an unbounded cylindrical domain, also called waveguide, from boundary measurements. More precisely, we prove recovery of a general class of electric potentials from the partial Dirichlet-to-Neumann map, where the Dirichlet data is supported on slightly more than half of the boundary and the Neumann data is taken on the other half of the boundary. We apply this result in different contexts including recovery of some general class of non-compactly supported coefficients from measurements on a bounded subset and recovery of an electric potential, supported on an unbounded cylinder, of a Schrödinger operator in a slab.
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