Kirchhoff型方程变号解的存在性

Existence of Nodal Solutions for Kirchhoff Type Equations

近年来,许多学者通过节点Nehari流形的方法研究了带有非线性项f(x,u)的Kirchhoff型方程的变号解的存在性,其中f(x,u)具有3阶超线性增长。然而对于22情况下Kirchhoff型方程的变号解的存在性。

In recent years, the existence of nodal solutions for Kirchhoff equations with the nonlinearity f(x,u) with superlinear 3-growth in Ω ( maybe a bounded domain or R3) can be established by the nodal Nehari manifold approach, however, for the case where 2, such an approach is not applied directly because Palais-Smale sequence restricted on the nodal Nehari manifold is not bounded. In this paper, through using the refined Nehari manifold methods, we are devoted to prove the existence of sign-changing solutions for a class of Kirchhoff type problems in the case where 2.