Ground State Solutions for Robin Concave–Convex Problems with Unbalanced Growth

We consider a nonlinear Robin problem driven by a differential operator with unbalanced growth and a reaction which exhibits the competing effects of a parametric concave (sublinear) term and of a convex (superlinear) term. Using the Nehari method, we show that for all small values of the parameter, the problem has two bounded, ground state (least energy) solutions. In the process of the proof, we establish some auxiliary results which are of independent interest.