The Existence And Concentration Of Solutions For Fractional Schr(?)dinger-Poisson System And Klein-Gordon-Maxwell System

Fractional Schr(?)dinger-Poisson system is one of the research objects in the field of nonlinear analysis in recent years,which derived from fractional quantum mechanics.In this thesis,we study the existence,multiplicity and concentration phenomenon of solutions for the fractional Schr(?)dinger-Poisson system and the fractional Klein-Gordon-Maxwell system via the variational methods.Firstly,we prove the existence of the ground state solutions of a class of fractional Schr(?)dinger-Poisson system with deep potential well and the asymptotic of the ground state solutions as the parameter goto infinity.Secondly,we show the existence of a ground state solution of a class of asymptotical peridoic fractional Schr(?)dinger-Poisson system by using the concentration-compactness and the non-smooth Nehari manifold method developed by Szulkin and Weth.Finally,under some mild assumptions,we obtain two different nontrivial soltuions of a class of the fractional Klein-Gordon-Maxwell sytem.In addition,we show that these solutions concentrate around the bottom of the potential well as the parameter large enough.