Existence and multiplicity results for Kirchhoff type problems with four-superlinear potentials

Abstract

In this article, we study the existence and multiplicity results for Kirchhoff type equations of the form where is three-superlinear at infinity. Under certain assumptions on f, we obtain at least one nontrivial solution for (*) without assuming the Ambrosetti and Rabinowitz condition by using the mountain pass theorem, and obtain infinitely many solutions when f(x, ·) is odd by using the fountain theorem.