Infinitely many sign-changing solutions to a conformally invariant integral equation on [formula omitted

Abstract

In this work we consider the Euler–Lagrange equation for the critical points of a functional related to the conformal exponent case of the classical Hardy–Littlewood–Sobolev inequality. By lifting the problem to the sphere and leveraging the symmetries of the lifted problem, the existence of an unbounded sequence of sign-changing solutions is established. As a consequence, the existence of an unbounded sequence of sign-changing solutions to a non linear system of equations involving the fractional Laplacian is obtained.