Existence of nontrivial solutions for p-Laplacian variational inclusion systems in ℝ ^N

Abstract

The authors study the existence of nontrivial solutions to p-Laplacian variational inclusion systems \left\{ \begin{gathered} - \Delta _p u + \left| u \right|^{p - 2} u \in \partial _1 F\left( {u,v} \right), in \mathbb{R}^N , \hfill \\ - \Delta _p v + \left| v \right|^{p - 2} v \in \partial _2 F\left( {u,v} \right), in \mathbb{R}^N , \hfill \\\end{gathered} \right. where N ≥ 2, 2 ≤ p ≤ N and F: ℝ² → ℝ is a locally Lipschitz function. Under some growth conditions on F, and by Mountain Pass Theorem and the principle of symmetric criticality, the existence of such solutions is guaranteed.

Keywords

Mountain pass theorem / p-Laplacian / Principle of symmetric criticality / Variational inclusion systems / (PS)-condition / Locally Lipschitz functions

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