Multiple solutions for the nonhomogeneous Kirchhoff equation on RN

In this paper we study the following nonhomogeneous Kirchhoff equation −(a+b∫RN|∇u|2dx)Δu+V(x)u=f(x,u)+h(x),inRN, where ff satisfies the Ambrosetti–Rabinowitz type condition. Under appropriate assumptions on VV, ff and hh, the existence of multiple solutions is proved by using the Ekeland’s variational principle and the Mountain Pass Theorem in critical point theory.