The Existence Of Two Kinds Of Schrödinger System Solutions

In this paper, we study the existence of solutions of two Schrodinger systems.In Chapter 1, we study the nonhomogeneous Schrodinger-Maxwell problems in R3. where F(u.v) is a C1 function,2< ?< 6, ?1,?2> 0,0?g(x),h(x) are radially symmetric functions. By using variational methods, we prove that the problems have at least two solutions provided that ?2 max{||g||2,||h||2}?ca.In Chapter 2, we study the Schrodinger-Possion system in R3. where 1< p< 6, and p?2,4. Assuming that a:R3?R and K:R3?R are continuous functions and satisfyig suitable assumptions, we obtain the existence of weak solutions for the above system by using one dimensional fibering method.