Sign-Changing Solutions for Nonlinear Elliptic Problems Depending on Parameters

D. Motreanu () and V. V. Motreanu ()
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D. Motreanu: Université de Perpignan
V. V. Motreanu: Ben Gurion University of the Negev

A chapter in Handbook of Functional Equations, 2014, pp 327-364 from Springer

Abstract: Abstract This chapter is concerned with parametric Dirichlet boundary value problems involving the p-Laplacian operator. Specifically, this chapter gives an account of recent results that establish the existence and multiplicity of solutions according to different types of nonlinearities in the problem. More precisely, we focus on problems exhibiting nonlinearities of concave–convex type and nonlinearities that are asymptotically $(p-1)$ -linear. In each situation, we point out significant qualitative properties of the solutions, especially, we establish the existence of sign-changing (that is, nodal) solutions.

Keywords: Elliptic equation; Boundary value problem; p-Laplacian; Variational method; Upper and lower solutions; Sign-changing solution (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-1-4939-1246-9_15

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DOI: 10.1007/978-1-4939-1246-9_15

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