The Existence Of Ground State Positive Solutions For A P-Kirchhoff Type Problem In R~N

In this paper, we study the existence of positive solutions to the following nonlinear p-Kirchhoff type equation with a periodic potential as well as a asymptotically periodic potential, where a,b>0are two constants,1<p<N<p2/p-1, is p-Laplacian operator. V:RNâ†'R is a bounded locally Holder continuous function.f∈C1(R, R) is subcritical and superlinear at s=0as well as at s=∞. Under the strict monotonicity of the function, using Nehari manifold and Mountai Pass Lemma, we prove the existence of positive ground states without assuming the Ambrosetti-Rabinowitz type condition. Our main result extends partially a result about the nonlinear Kirchhoff type problem in R3by X. He and W. Zou in [13] to the nonlinear p-Kirchhoff type equation. In the mean time, assumptions on â…¤(x) in this paper are more general than that in [15].