Multiple solutions for quasilinear elliptic problems with concave-convex nonlinearities in Orlicz–Sobolev spaces

Abstract

Using variational arguments, we establish the existence of two nontrivial solutions for quasilinear elliptic problems in Orlicz-Sobolev spaces, where the nonlinear terms exhibit the combined effects of concave and convex without the Ambrosetti-Rabinowitz type condition.