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.