Existence of nontrivial solutions for p-Laplacian variational inclusion systems in ℝN

The authors study the existence of nontrivial solutions to p-Laplacian variational inclusion systems \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\left\{ \begin{gathered} - \Delta _p u + \left| u \right|^{p - 2} u \in \partial _1 F\left( {u,v} \right), in \mathbb{R}^N , \hfill \\ - \Delta _p v + \left| v \right|^{p - 2} v \in \partial _2 F\left( {u,v} \right), in \mathbb{R}^N , \hfill \\ \end{gathered} \right.$\end{document} 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.