M. Kh. Chankaev, A. B. Shabat, “A nonlinear eigenvalue problem”, TMF, 157:2 (2008), 175–187; Theoret. and Math. Phys., 157:2 (2008), 1514

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Teoreticheskaya i Matematicheskaya Fizika, 2008, Volume 157, Number 2, Pages 175–187
DOI: https://doi.org/10.4213/tmf6273 (Mi tmf6273)

This article is cited in 20 scientific papers (total in 20 papers)

A nonlinear eigenvalue problem

M. Kh. Chankaev^a, A. B. Shabat^b

^a Karachay-Cherkess State University
^b L. D. Landau Institute for Theoretical Physics, Russian Academy of Sciences

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DOI: https://doi.org/10.4213/tmf6273

Abstract: We reduce the problem of the zeros of an entire function related to the Painlevé I equation to the eigenvalue problem for the Dirichlet problem for a fourth-order bilinear equation. In a simplified case, this problem reduces to the problem of the position of the zeros of theta functions. We then apply the developed general method to the inverse scattering problem.

Keywords: entire function, Painlevé transcendent, inverse scattering problem.

Received: 13.02.2008

English version:
Theoretical and Mathematical Physics, 2008, Volume 157, Issue 2, Pages 1514–1524
DOI: https://doi.org/10.1007/s11232-008-0126-4

Bibliographic databases:

Language: Russian

Citation: M. Kh. Chankaev, A. B. Shabat, “A nonlinear eigenvalue problem”, TMF, 157:2 (2008), 175–187; Theoret. and Math. Phys., 157:2 (2008), 1514–1524

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This publication is cited in the following 20 articles:

Sabina De Lis J.C., “Remarks on the Second Neumann Eigenvalue”, Electron. J. Differ. Equ., 2022:13 (2022)
Sabina de Lis J.C., Segura de Leon S., “P-Laplacian Diffusion Coupled to Logistic Reaction: Asymptotic Behavior as P Goes to 1”, Ann. Mat. Pura Appl., 2022
Kurki E.-K., Vahakangas A.V., “Weighted Norm Inequalities in a Bounded Domain By the Sparse Domination Method”, Rev. Mat. Complut., 34:2 (2021), 435–467
Hynd R., Lindgren E., “Large Time Behavior of Solutions of Trudinger'S Equation”, J. Differ. Equ., 274 (2021), 188–230
Sabina De Lis J.C., Segura De Leon S., “The Limit as P -> 1 of the Higher Eigenvalues of the P-Laplacian Operator -Delta(P)”, Indiana Univ. Math. J., 70:4 (2021), 1395–1439
Alluhaibi N., Ali A., “The Eigenvalue Estimates of P-Laplacian of Totally Real Submanifolds in Generalized Complex Space Forms”, Ric. Mat., 2021
Mukherjee Sh., “On Minimax Characterization in Non-Linear Eigenvalue Problems”, Bruno Pini Math. Anal. Semin., 12:1 (2021), 81–100
Manfredi G., “Is the Cosmological Constant An Eigenvalue?”, Gen. Relativ. Gravit., 53:3 (2021), 31
Farcaseanu M., Grecu A., Mihailescu M., Stancu-Dumitru D., “Perturbed Eigenvalue Problems: An Overview”, Stud. Univ. Babes-Bolyai Math., 66:1 (2021), 55–73
Esposito L., Roy P., Sk F., “On the Asymptotic Behavior of the Eigenvalues of Nonlinear Elliptic Problems in Domains Becoming Unbounded”, Asymptotic Anal., 123:1-2 (2021), 79–94
Colbois B., Provenzano L., “Conformal Upper Bounds For the Eigenvalues of the P-Laplacian”, J. Lond. Math. Soc.-Second Ser., 104:5 (2021), 2128–2147
de la Calle Ysern B., Sabina de Lis J.C., Segura de Leon S., “The Convective Eigenvalues of the One-Dimensional P-Laplacian as P -> 1”, J. Math. Anal. Appl., 484:1 (2020), 123738
Hoeg F.A., “Concave Power Solutions of the Dominative P-Laplace Equation”, NoDea-Nonlinear Differ. Equ. Appl., 27:2 (2020), 19
El-Ferik S., Al-Rawashdeh Ya.M., Lewis F.L., “A Framework of Multiagent Systems Behavioral Control Under State-Dependent Network Protocols”, IEEE Trans. Control Netw. Syst., 7:2 (2020), 734–746
Khaled M., Rhoudaf M., Sabiki H., “Lagrange Multiplier Rule to a Nonlinear Eigenvalue Problem in Musielak-Orlicz Spaces”, Numer. Funct. Anal. Optim., 41:2 (2020), 134–157
Bozorgnia F., Mohammadi S.A., Vejchodsky T., “The First Eigenvalue and Eigenfunction of a Nonlinear Elliptic System”, Appl. Numer. Math., 145 (2019), 159–174
Fusco N., Mukherjee Sh., Zhang Y.R.-Ya., “A Variational Characterisation of the Second Eigenvalue of the P-Laplacian on Quasi Open Sets”, Proc. London Math. Soc., 119:3 (2019), 579–612
Chiappinelli R., “Nonlinear Rayleigh Quotients and Nonlinear Spectral Theory”, Symmetry-Basel, 11:7 (2019), 928
Della Pietra F., Gavitone N., Piscitelli G., “On the Second Dirichlet Eigenvalue of Some Nonlinear Anisotropic Elliptic Operators”, Bull. Sci. Math., 155 (2019), 10–32
V. Yu. Novokshenov, “Padé approximations for Painlevé I and II transcendents”, Theoret. and Math. Phys., 159:3 (2009), 853–862

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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