Arbitrarily many solutions for a perturbed p(x)p(x)-Laplacian equation involving oscillatory terms

This paper deals with a perturbed p(x)p(x)-Laplacian equation involving oscillatory terms:-div|∇u|p(x)-2∇u+|u|p(x)-2u=Q(x)f(u)+εg(u)x∈RN,u⩾0,u(x)→0as|x|→∞.By using variational methods and the non-smooth version symmetric criticality principle, we establish (a) the unperturbed problem P0P0 has infinitely many distinct solutions; (b) the number of distinct solutions for PεPε becomes greater and greater whenever εε is smaller and smaller. Our results are a generalization of the case of Laplacian from Kristály to the case of p(x)p(x)-Laplacian.