Infinitely many solutions for a nonlinear Navier boundary systems involving $(p(x),q(x))$-biharmonic

Abstract

In this article, we study the following $(p(x),q(x))$-biharmonic type system
\begin{gather*}
\Delta(|\Delta u|^{p(x)-2}\Delta u)=\lambda F_u(x,u,v)\quad\text{in }\Omega,\\
\Delta(|\Delta v|^{q(x)-2}\Delta v)=\lambda F_v(x,u,v)\quad\text{in }\Omega,\\
u=v=\Delta u=\Delta v=0\quad  \text{on }\partial\Omega.
\end{gather*}
We prove the existence of infinitely many solutions of the problem by
applying a general variational principle due to B. Ricceri and the theory of the variable exponent Sobolev spaces.