Existence and nonexistence results for weighted fourth order eigenvalue problems with variable exponent

Abstract

This paper presents sufficient conditions for the existence and nonexistence of eigenvalues for a $p(x)$-biharmonic equation with Navier boundary conditions and weight function on a bounded domain in $\mathbb{R}^N$. Our approach is mainly based on a adequate variational techniques.

Keywords

• Fourth order elliptic equation
• variable exponent
• indefinite weight
• eigenvalue problem