Anisotropic Robin problems with indefinite potential

Abstract

We considered a nonlinear elliptic boundary value problem driven by the variable (anisotropic) (p, q)-Laplacian with Robin boundary condition and a superlinear reaction which does not satisfy the Ambrosetti-Rabinowitz condition. Using critical point theory, truncation and comparison techniques and critical groups, we showed the existence of five nontrivial smooth solutions all with sign information and ordered.