Research On The Existence And Multiplicity Of Solutions Of Schr(?)dinger-Born-Infeld System

The main purpose of this thesis is to investigate the existence and multiplicity of nontrivial solutions for the following Schr(?)dinger-Born-Infeld system:where f is the nonlinear term.The main contents are as follows:The first chapter introduces the background and the latest research developments of Schr(?)dinger-Born-Infeld system.Furthermore,the main research contents and relevant preparatory knowledge of this paper are elaborated.The second chapter studies the case that f is superlinear and subcritical at infinity.And when f is an odd function,we obtain the existence of infinitely many radial solutions of the system by combining the invariant set and Ljustinik-Schnirelman type minimax method.The third chapter studies the nonhomogeneous Schr(?)dinger-Born-Infeld system with a perturbation term g.By adding some appropriate constraints to the perturbation term and nonlinear term,we study the existence and multiplicity of solutions of the system by using the Ekeland variational principle,mountain pass theorem,perturbation method and truncation technique.The fourth chapter studies the Schr(?)dinger-Born-Infeld system with steep potential well,the existence and asymptotic behavior of nontrivial solutions are obtained by using the variational techniques.The fifth chapter presents the conclusions and outlook of this paper.