Existence results for p(x)-biharmonic problems involving a singular and a Hardy type nonlinearities

Abstract

In this paper, we proved the existence and the multiplicity of solutions for some $ p(x) $-biharmonic problems involving singular nonlinearity and a Hardy potential. More precisely, by the use of the min-max method, we proved the existence of a nontrivial solution for such a problem. Next, diversions of the mountain pass theorem were used to prove the multiplicity of solutions.

Keywords

• $ p(x) $-biharmonic operator
• singular equations
• variational methods
• mountain pass theorem
• existence