A multiplicity result for asymptotically linear Kirchhoff equations

Abstract

In this paper, we study the following Kirchhoff type equation: (equation presented) where N ≥ 3, b > 0 and f(s) is asymptotically linear at infinity, that is, f(s) ~ O(s) as s → +∞. By using variational methods, we obtain the existence of a mountain pass type solution and a ground state solution under appropriate assumptions on a(x).