On the existence of five nontrivial solutions for resonant problems with p-Laplacian

Leszek Gasiński; Nikolaos Papageorgiou

ArticleOriginal scientific text

Title

On the existence of five nontrivial solutions for resonant problems with p-Laplacian

Authors ¹, ²

Affiliations

Jagiellonian University, Institute of Computer Science, Poland
National Technical University, Department of Mathematics, Greece

Abstract

In this paper we study a nonlinear Dirichlet elliptic differential equation driven by the p-Laplacian and with a nonsmooth potential. The hypotheses on the nonsmooth potential allow resonance with respect to the principal eigenvalue λ₁ > 0 of

(- Δ ₚ, W ₀^{1, p} (Z))

. We prove the existence of five nontrivial smooth solutions, two positive, two negative and the fifth nodal.

Keywords

ENG

p-Laplacian, Clarke subdifferential, linking sets, upper-lower solutions, second eigenvalue, nodal and constant sign solutions, second deformation theorem

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Title

On the existence of five nontrivial solutions for resonant problems with p-Laplacian

Affiliations

Abstract

Keywords

Bibliography