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

Leszek GasińskiNikolaos S. Papageorgiou — 2010

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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 , W 1 , p ( Z ) ) . We prove the existence of five nontrivial smooth solutions, two positive, two negative and the fifth nodal.

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