Existence and multiplicity of nontrivial solutions of biharmonic equations via differential inclusion

Abstract

<p style='text-indent:20px;'>This paper is concerned with a class of biharmonic elliptic differential inclusion in <inline-formula><tex-math id="M1">\begin{document}$ \mathbb R^N $\end{document}</tex-math></inline-formula>. Under various growth conditions on the nonlinearity, new results on existence and multiplicity of solutions are derived. The main tools used in this paper are the nonsmooth version of mountain pass theorem and the generalized gradient for locally Lipschitz functionals.