Existence of three solutions for variable exponent elliptic systems (Q895818)

The author investigates the existence of solutions for the elliptic system \[ \Delta(|\Delta u|^{p(x)-2}\Delta u)=\lambda F_u(x,u,v)+\mu G_u(x,u,v), \] \[ \Delta(|\Delta v|^{q(x)-2}\Delta v)=\lambda F_v(x,u,v)+\mu G_v(x,u,v), \] in a smooth open and bounded subset of \({\mathbb R}^N\), \(N\geq 1\). The system is complemented with Navier boundary conditions. Under some additional conditions the author obtains the existence of at least three weak solutions. The approach relies on a three critical point theorem due to Ricceri.