Existence Of Ground State Solutions And Multiple Solutions For Schr(?)dinger-bopp-podolsky Systems

In this thesis,we study the existence of multiple solutions of Schr6dinger-BoppPodolsky(for short SBP)system and the existence of ground state solutions of nonautonomous SBP system by using the methods of variational method,symmetric Mountain pass theorem,Nehari manifold and splitting lemma.This thesis mainly considers several cases involved in R3.First,we study the non-autonomous Schrodinger-Bopp-Podolsky system:where a>0,γ>0,2<p<6 and both K(x)and b(x)are nonnegative functions in R3.Here we divide the study into two parts:Firstly,when p∈(4,6),the embedding compactness cannot be obtained in R3,so the split lemma is first used to recover the compactness of the bounded Palais-Smale sequence.At the same time,in order to find the critical point of the energy functional corresponding to the equation,the ground state solution of the SBP system is found by limiting it to a Nehari manifold and then searching for the minimum energy solution.Then when p∈(2,4],the method adopted in this section is to minimize the energy functional on M1(1)(cτ),and then the hypothesis about K(x)and b(x)is given.Then the boundedness of Palais-Smale sequence is obtained by means of Pohozaev identity,and the ground state solution is found by means of Nehari manifold method.Finally,we study the Schrodinger-Bopp-Podolsky system with coercive potential:where x∈R3,a>0,V(x)∈C(R3,R),f is a Superlinear function with subcritical growth,μ is a positive parameter.Since the equation is unbounded with critical growth,the coercive potential is used to ensure the compactness of the space.The convergence of Palais-Smale sequence is obtained by using the principle of concentrated compactness,and then the existence of multiple solutions of SBP system is obtained by means of the symmetric Mountain pass theorem.