Infinitely many solutions for a Kirchhoff problem with a subcritical exponent

Abstract

This article deals with the following Kirchhoff problem:(0.1)−(a+b∫RN|∇u|2)Δu+u=K(x)|u|p−1uinRN, where a, b>0, 1<p<2⁎−1, 2⁎=2NN−2, and K(x) is a potential function. We prove that problem (0.1) has infinitely many solutions by using Lyapunov-Schmidt reduction. Our results extend and improve the results for the Schrödinger equation obtained by Badiale (2002) [3].