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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.

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