分数阶自治Kirchhoff方程径向变号解的存在性

Existence of radial sign-changing solution for a fractional autonomous Kirchhoff equation

摘要:

本文考虑全空间上一类分数阶自治Kirchhoff方程变号解的存在性. 首先，我们证明了分数阶自治的Kirchhoff方程在适当条件下与一个分数阶自治Schrodinger系统等价；然后，利用分数阶自治Schrodinger方程的径向变号解的存在性结果，我们证明了分数阶自治的Schrodinger系统的解的存在性；最后，我们得到了分数阶自治的Kirchhoff方程径向变号解的存在性结果.

Abstract:

The existence of sign-changing solutions for a fractional autonomous Kirchhoff equation is considered in the whole space. We prove that this equation is equivalent to a fractional autonomous Schr&odinger system under appropriate conditions. Then, by using the existence of radial sign-changing solution of the fractional autonomous Schrodinger equation, the existence of solutions for the fractional autonomous Schrodinger system is proved. The existence of radial sign-changing solution for the fractional autonomous Kirchhoff equation is obtained as well.