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

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.