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

Abdesslem Ayoujil

doi:10.5269/bspm.v37i3.31657

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

Authors

Abdesslem Ayoujil University Mohammed I Regional Centre of Trades Education and Training Faculty of Science Department of Mathematics Laboratory Nonlinear Analysis

DOI:

https://doi.org/10.5269/bspm.v37i3.31657

Keywords:

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

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.