Existence of beam-equation solutions with strong damping and p(x)-biharmonic operator

Abstract

In this paper, we consider a nonlinear beam equation with a strong damping and the p(x)-biharmonic operator. The exponent p(·) of nonlinearity is a given function satisfying some condition to be specified. Using Faedo-Galerkin method, the local and global existence of weak solutions is established with mild assumptions on the variable exponent p(·). This work improves and extends many other results in the literature.