Multiple positive solutions for Kirchhoff type problems involving concave-convex nonlinearities

Abstract

In this paper, we are interested in looking for multiple solutions for a class of Kirchhoff type problems with concave-convex nonlinearities. Under the combined effect of coefficient functions of concave-convex nonlinearities, by the Nehari method, we obtain two solutions, and one of them is a ground state solution. Under some stronger conditions, we point that the two solutions are positive solutions by the strong maximum principle.