Ground state sign-changing solutions for asymptotically 3-linear Kirchhoff-type problems

Abstract

This paper is devoted to the existence of ground state sign-changing solutions for a class of Kirchhoff-type problems(Section.Display) where is a bounded domain with a smooth boundary , , and satisfies asymptotically linear growth that is very different from super-3-linear growth in previous literatures. Without assuming the standard Variant Nehari-type condition related to (0.1), we prove that (0.1) possesses one ground state sign-changing solution , and show that its energy is strictly larger than twice that of the ground-state solutions of Nehari-type. Furthermore, we establish the convergence property of as the parameter .