Existence Results for a Generalized $p$($x$)-Biharmonic Problem Type with No-Flux Boundary Condition

Abstract

This paper aims to study the existence and multiplicity of weak solutions for a problem involving a generalized $p$($x$)-biharmonic operator with no flux boundary condition. By using the variational techniques and the theory of the variable exponent Lebesgue spaces, we obtain the existence of at least one nontrivial solution and at least $n$ distinct pairs of nontrivial weak solutions to this problem, respectively.