Nonexistence of ground state sign-changing solutions for autonomous Schrodinger-Poisson system with critical growth

This paper is concerned with the following Schrodinger-Poisson system {-Delta u + u + phi u = vertical bar u vertical bar(p-1)u + vertical bar u vertical bar(4)u, x is an element of R-3, - Lambda phi = u(2), x is an element of R-3, where 3< p< 5. With the help of an odd Nehari manifold and 'energy doubling' property, we prove the nonexistence of ground state sign-changing solutions on H-1(R-3). In this sense, our result explains why the existing literature can only consider the existence of the ground state sign-changing solutions in the radial Sobolev space H-r(1)(R-3).