Least energy nodal solutions for Kirchhoff‐type Laplacian problems

Abstract

In this paper, we are concerned with the existence of least energy nodal solutions for the following Kirchhoff‐type Laplacian problems: where is a bounded domain with a smooth boundary , , , and . In the light of characteristics of the Kirchhoff‐type function , we impose a weaker assumption on instead of the usual Nehari type monotonicity condition and then prove the existence of one least energy nodal solution of Equation by applying constraint variational method, quantitative deformation lemma as well as one variant of Miranda theorem. Moreover, we show that the energy of nodal solution is strictly larger than twice of that of any ground state solutions of Nehari type to Equation and also study the convergence property of as the parameter . Our results improve and extend the known results of the usual case in the sense that a more wider rang of is covered.