Existence and multiplicity of solutions for a class ofp-Laplacian equations

Existence and Multiplicity of Solutions for p(x)-LaplacianEquations in $${\mathbb {R}}^N$$ R N

“…But this condition is very restrictive eliminating many nonlinearities. In this paper, we introduce a new condition (F1) (motivated by [10]), below, which is different from the Ambrosetti-Rabinowitz-type condition (F1 ). …”