Positive and sign-changing solutions of a Schr?dinger-Poisson system involving a critical nonlinearity

摘要

In this paper, we consider the Schr?dinger-Poisson system, where μ is a positive constant and the nonlinear growth of |u|~4u reaches the Sobolev critical exponent since 2~*=6 for three spatial dimensions. We prove the existence of at least a pair of fixed sign solutions and a pair of sign-changing solutions in H~1(R~3)×D~(1,2)(R~3) under some suitable conditions on the nonnegative functions l, k and h, but not requiring any symmetry properties on them.