A Fourth Order Singular Elliptic Problem Involving $p$-biharmonic Operator

Abstract

In this paper, a fourth order singular elliptic problem involving $p$-biharmonic operator with Dirichlet boundary condition is considered. The existence of at least one weak solution is proved in two different cases of the nonlinear term at the origin. The results are obtained by applying the critical points principle of Ricceri, variational methods and Rellich's inequality. Also an example is presented to verify the results.