Solutions for parametric double phase Robin problems

Abstract

We consider a parametric double phase problem with Robin boundary condition. We prove two existence theorems. In the first the reaction is ( p - 1 )-superlinear and the solutions produced are asymptotically big as λ → 0 + . In the second the conditions on the reaction are essentially local at zero and the solutions produced are asymptotically small as λ → 0 + .