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

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Schr?dinger系统等价;然后,利用分数阶自治Schr?dinger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Schr?dinger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.

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