A weighted (p,2)-equation with double resonance
DOI:
https://doi.org/10.58997/ejde.2023.30Keywords:
Constant sign and nodal solutions, nonlinear regularity, nonlinear maximum principle, critical groups, spectrum of weighted r-Laplacian, double resonanceAbstract
We consider a Dirichlet problem driven by a weighted (p,2)-Laplacian with a reaction which is resonant both at \(\pm\infty\) and at zero (double resonance). We prove a multiplicity theorem producing three nontrivial smooth solutions with sign information and ordered. In the appendix we develop the spectral properties of the weighted r-Laplace differential operator.
For more information see https://ejde.math.txstate.edu/Volumes/2023/30/abstr.html
References
S. Aizicovici, N. S. Papageorgiou, V. Staicu; Degree Theory for Operators of Monotone Type and Nonlinear Elliptic Equations with Inequality Constraints, Memoirs AMS 196 (No. 915), 2008, pp. 70. https://doi.org/10.1090/memo/0915
K. C. Chang; Infinite Dimensional Morse Theory and Multiple Solution Problems, Birkhäuser, Boston, 1993. https://doi.org/10.1007/978-1-4612-0385-8
D. de Figueiredo, J. Gossez; Strict monotonicity of eigenvalues and unique continuation, Commun. Partial Diff. Equ. 17 (1992), 339-346. https://doi.org/10.1080/03605309208820844
M. Filippakis, N. S.Papageorgiou; Multiple constant sign and nodal solutions for nonlinear elliptic equations with the p-Laplacian, J. Differential Equ. 245 (2008), 1883-1922. https://doi.org/10.1016/j.jde.2008.07.004
L. Gasinśki, N. S. Papageorgiou; Nonlinear Analysis, Series in Mathematical Analysis and Applications, 9. Chapman & Hall/CRC, Boca Raton, FL, 2006.
L. Gasinśki, N. S. Papageorgiou; Exercises in Analysis. Part 2, Nonlinear Analysis. Problem Books in Mathematics. Springer, Cham, 2016. viii+1062 pp.
L. Gasinśki, N. S. Papageorgiou; Positive solutions for the Robin p-Laplacian with competing nonlinearities, Adv. Calc. Var. 12 (2019), 31-56. https://doi.org/10.1515/acv-2016-0039
S. Hu, N. S. Papageorgiou; Research Topics in Analysis. Volume I: Grounding Theory, Birkhäuser, Cham, 2022. https://doi.org/10.1007/978-3-031-17837-5
J. Jaros; A harmonic Picone's Identity with applications, Annoili Mat. Pura Appl. 194 (2015), 719-729. https://doi.org/10.1007/s10231-013-0394-y
O. A. Ladyzhenskaya, N. N. Uraltseva; Linear and quasilinear elliptic equations, Translated from the Russian by Scripta Technica, Inc. Translation editor: Leon Ehrenpreis Academic Press, New York-London 1968 xviii+495 pp.
G. Lieberman; The natural generalization of the natural conditions of Ladyzhenskaya and Ural'tseva for elliptic equations, Comm. Partial Differential Equations 16 (1991), 311-361. https://doi.org/10.1080/03605309108820761
Z. H. Liu, N. S. Papageorgiou; Superlinear weighted (p, q)-equations with indefinite potential, J. Convex Anal. 28 (2021), 967-982.
Z. H. Liu, N. S. Papageorgiou; Nodal solutions for a weighted (p, q)-equations, J. Convex Anal. 29 (2022), 559-570.
Z. H. Liu, N. S. Papageorgiou; Dirichlet (p, q)-equations with gradient dependent and locally defined reaction, Electron. J. Differential Equations, 2021 (2021), no. 34, 1-8. https://doi.org/10.1088/1361-6544/ac0612
R. S. Palais; Homotopy theory of infinite dimensional manifolds, Topology 5 (1966), 1-16. https://doi.org/10.1016/0040-9383(66)90002-4
N. S. Papageorgiou, V. D. Rădulescu, D. Repovš; Nonlinear Analysis-Theory and Methods, Springer Nature, Swizerland AG, 2019. https://doi.org/10.1007/978-3-030-03430-6
N. S. Papageorgiou, V. D. Rădulescu, Y. Zhang; Anisotropic singular double phase problems, Discr. Cont. Dynam. Systems-S, 14 (2021), 4465-4502. https://doi.org/10.3934/dcdss.2021111
N. S. Papageorgiou, P. Winkert; Applied Nonlinear Functional Analysis, De Gruyter, Berlin, 2018. https://doi.org/10.1515/9783110532982
P. Pucci, J. Serrin; The Maximum Principle, Birkhäuser, Basel, 2007. https://doi.org/10.1007/978-3-7643-8145-5
Z. Q. Wang; On a superlinear elliptic equation, AIHP-Analyse Nonlineaire, 8 (1991) 43-58. https://doi.org/10.1016/s0294-1449(16)30276-1
Downloads
Published
License
Copyright (c) 2023 Zhenhai Liu, Nikolaos S. Papageorgiou
This work is licensed under a Creative Commons Attribution 4.0 International License.
