Infinitely many solutions for a Schrödinger–Kirchhoff equations with concave and convex nonlinearities

This paper is concerned with the following Schrödinger–Kirchhoff equation −(a+b∫R3|∇u|2dx)Δu+V(x)u=k(x)|u|q−2u−h(x)|u|p−2u,u∈H1(R3),where a and b are positive constants, 1<q<2<p<+∞. Under some suitable assumptions on V(x), k(x) and h(x), we obtain the existence of multiple solutions for this problem via a variant of Clark's theorem.