Research On The Existence And Multiplicity Of Solutions For Schr(?)dinger-Poisson Systems

The main purpose of this paper is to investigate the existence and multiplicity of nontrivial solutions for two class of Schr(?)dinger-Poisson systems by using the Variational methods.The main contents are as follows:The first chapter introduces the background and the latest research developments of Schr(?)dinger-Poisson system.Furthermore,the main research contents and relevant preparatory knowledge of this paper are elaborated.The second chapter studies the following Schr(?)dinger-Poisson system with a perturbation term(?)When the potential V(x)and the nonlinearity term f(x,u)satisfy some suitable assumptions,we obtain the multiplicity of nontrivial solutions for the above Schr(?)dinger-Poisson system via Ekeland variational principle and Mountain pass lemma if ‖h‖2 is small enough.The third chapter studies the following Krichhoff-Schr(?)dinger-Poisson system with periodic potential(?)When the nonlinearity term f(x,u)satisfies some suitable assumptions,we obtain the existence of ground states for the above system by using the Nehari manifold reduction method and concentration-compactness principle.The fourth chapter presents the conclusions and outlook of this paper.