Multiple solutions for eigenvalue problems involving the (p, q)–Laplacian
DOI:
https://doi.org/10.24193/subbmath.2023.1.07Keywords:
Eigenvalue problems, (p, q)–Laplacian, multiple solutions.Abstract
This paper is devoted to a subject that Professor Csaba Varga suggested during his frequent visits to the University of Perugia and in my regular stays at the “Babe¸s-Bolyai” University. More specifically, continuing the work started in [7] jointly with Professor Varga, here we establish the existence of two nontrivial (weak) solutions of some one parameter eigenvalue (p, q)–Laplacian problems under homogeneous Dirichlet boundary conditions in bounded domains of RN .
Mathematics Subject Classification (2010): 35P30, 35J70, 35J60, 35J25, 35J62.
Received 22 September 2022; Revised 24 January 2023. Published Online: 2023-03-20. Published Print: 2023-04-30
References
Arcoya, D., Carmona, J., A nondifferentiable extension of a theorem of Pucci and Serrin and applications, J. Differential Equations, 235(2007), 683–700.
Barbu, L., Moroșanu, G., Full description of the eigenvalue set of the Steklov (p, q)–Laplacian, J. Differential Equations, 290(2021), 1–16.
Berger, M.S., Nonlinearity and Functional Analysis, Lectures on Nonlinear Problems in Mathematical Analysis, Pure and Applied Mathematics, Academic Press, New York–London, 1977.
Bobkov, V., Tanaka, M., Multiplicity of positive solutions for (p, q)–Laplace equations with two parameters, Commun. Contemp. Math., 24(2022), no. 3, Paper No. 2150008, 25 pp.
Brézis, H., Functional Analysis, Sobolev Spaces and Partial Differential Equations, Universitext, Springer, New York, 2011.
Colasuonno, F., Pucci, P., Multiplicity of solutions for p(x)–polyharmonic elliptic Kirchhoff equations, Nonlinear Anal., 74(2011), no. 17, 5962–5974.
Colasuonno, F., Pucci, P., Varga, C., Multiple solutions for an eigenvalue problem involving p–Laplacian type operators, Nonlinear Anal., 75(2012), no. 12, 4496–4512.
Colasuonno, F., Squassina, M., Eigenvalues for double phase variational integrals, Ann. Mat. Pura Appl., 195(2016), no. 6, 1917–1959.
Cuesta, M., Eigenvalue problems for the p–Laplacian with indefinite weights, Electron. J. Differential Equations, 2001(2001), 1–9.
Demengel, F., Hebey, E., On some nonlinear equations involving the p–Laplacian with critical Sobolev growth, Adv. Differential Equations, 3(1998), 533–574.
Kristály, A., Lisei, H., Varga, Cs., Multiple solutions for p–Laplacian type equations, Nonlinear Anal., 68(2008), 1375–1381.
Kristály, A., Rădulescu, V. Varga, Cs., Variational Principles in Mathematical Physics, Geometry, and Economics, Encyclopedia of Mathematics and its Applications, 136, Cambridge University Press, Cambridge, 2010.
Kristály, A., Varga, Cs., Multiple solutions for elliptic problems with singular and sublinear potentials, Proc. Amer. Math. Soc., 135(2007), 2121–2126.
Marano, S., Mosconi, S., Some recent results on the Dirichlet problem for (p, q)–Laplacian equation, Discrete Contin. Dyn. Syst. Ser. S, 11(2018), 279–291.
Marano, S., Mosconi, S., Papageorgiou, N.S., Multiple solutions to (p, q)–Laplacian problems with resonant concave nonlinearity, Adv. Nonlinear Stud., 16(2016), 51–65.
Marano, S., Mosconi, S., Papageorgiou, N.S., On a (p, q)–Laplacian problem with parametric concave term and asymmetric perturbation, Rend. Lincei Mat. Appl., 29(2018), 109–125.
Mingione, G.; Rădulescu, V., Recent developments in problems with nonstandard growth and nonuniform ellipticity, J. Math. Anal. Appl., 501(2021), Paper No. 125197, 41 pp.
Papageorgiou, N.S., Qin, D., R˘adulescu, V., Nonlinear eigenvalue problems for the (p, q)–Laplacian, Bull. Sci. Math., 172(2021), Paper No. 103039, 29 pp.
Pucci, P., Saldi, S., Multiple Solutions for an Eigenvalue Problem Involving Non–Local Elliptic p–Laplacian Operators, Geometric methods in PDE’s, 159–176, Springer INdAM Ser., 13, Springer, Cham, 2015.
Tanaka, M., Generalized eigenvalue problems for (p, q)–Laplacian with indefinite weight, J. Math. Anal. Appl., 419(2014), 1181–1192.
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