Least energy sign-changing solutions for a class of nonlocal Kirchhoff-type problems

Abstract

In this paper, we consider the existence of least energy sign-changing solutions for a class of Kirchhoff-type problem where is a bounded domain in , , with a smooth boundary , and . By using variational approach and some subtle analytical skills, the existence of the least energy sign-changing solutions of is obtained successfully. Moreover, we prove that the energy of any sign-changing solutions is larger than twice that of the ground state solutions of .

Existence of nonnegative nontrivial solutions for Kirchhoff type problems with variable exponent

“…Cheng [17] obtained the existence of one least energy sign‐changing solution for problem () by condition $$$ (S) $$$ and some extra assumptions. It is worth mentioning that the above conditions are usually for the non‐degenerate case, that is, the case $$$ a>0 $$$.…”

The Existence of the Sign-Changing Solutions for the Kirchhoff-Schrödinger-Poisson System in Bounded Domains

“…In fact, the studies about the existence of the positive solutions, signchanging solutions for a class of elliptic equations, have been studied extensively. For more details about such problems, we refer the reader to [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19].…”