LEAST ENERGY SIGN-CHANGING SOLUTIONS FOR SUPER-QUADRATIC SCHRODINGER-POISSON SYSTEMS IN R3

In this paper, we study the following Schrodinger-Poisson systems {-Delta u + Vu + lambda phi u = f(u), x is an element of R-3, -Delta phi = u(2), x is an element of R-3, where V, lambda > 0 and f is an element of C (R, R). Under some relaxed assumptions on f, using variational methods in combination with the Pohozaev identity, we prove that the above system possesses a least energy sign-changing solution and a ground state solution provided that lambda is sufficiently small. Moreover, we prove that the energy of a sign-changing solution is strictly larger than that of the ground state solution. Our results generalize and extend some recent results in the literature.