Existence of Solutions for Modified Schrodinger-Poisson System with Critical Nonlinearity in R-3

摘要

In this paper, we study the existence and multiplicity of semiclassical solutions of a modified version of the Schrodinger-Poisson system with critical nonlinearity in R-3. Under some given conditions which are given in Section 1, we prove that the problem has at least one nontrivial solution provided that <= epsilon and that for any n* epsilon N, it has at least n* pairs of solutions if epsilon <= epsilon(n*) where epsilon and epsilon(n*) are sufficiently small positive numbers. Moreover, these solutions u(epsilon), -> 0 in H-1(R-3) as epsilon -> 0.