Least energy sign-changing solutions for Kirchhoff-type problems with potential well

Abstract

In this paper, we investigate the existence of least energy sign-changing solutions for the Kirchhoff-type problem [Formula: see text], where a, b > 0 are parameters, [Formula: see text], and [Formula: see text]. Under weaker assumptions on V and f, by using variational methods with the aid of a new version of global compactness lemma, we prove that this problem has a least energy sign-changing solution with exactly two nodal domains, and its energy is strictly larger than twice that of least energy solutions.

On Kirchhoff-Type Equations with Hardy Potential and Berestycki–Lions Conditions

“…Because the Kirchhoff-type equation has a wide range of applications in many fields, such as it models several physical and biological systems, it has been widely considered in the last two decades by using variational methods, see [1][2][3][4][5][6][7][8][9][10][11] and references therein. We just introduce several results closely related to Equation (1) here.…”

Existence and concentration of least energy sign-changing solutions for critical Kirchhoff-type equations with a steep potential well

“…The existence of positive solutions, multiple solutions and ground state solutions of (3) have attracted extensive attention of scholars, for example, see [6,13,15,24,25,28,36]. Moreover, for more results about sign-changing solutions for Kirchhofftype equation with subcritical growth, see [8,10,22,31,39,40,41]. As far as we know, there are few articles on the existence of sign-changing solutions for Kirchhofftype equation with critical growth, such as [12,35,38,43,44,45].…”