Existence Of Solutions For Two-dimensional Schr(?)dinger-Poisson Equations

In this thesis,we mainly study the existence and multiplicity of solutions for the following planar Schr(?)dinger-Poisson system#12 where γ>0 is a constant,V:R2→R is a continuous function,g:R→R is a nonlinear function.If V(x)and g(u)satisfying certain conditions,by using variational methods,we prove the existence and multiplicity of solutions for equation(0.1).