Three solutions for a Neumann partial differential inclusion via nonsmooth Morse theory

Colasuonno, Francesca;Iannizzotto, Antonio;Mugnai, Dimitri

2017-01-01

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Abstract

We study a partial differential inclusion, driven by the p-Laplacian operator, involving a p-superlinear nonsmooth potential, and subject to Neumann boundary conditions. By means of nonsmooth critical point theory, we prove the existence of at least two constant sign solutions (one positive, the other negative). Then, by applying the nonsmooth Morse identity, we find a third non-zero solution.