Dynamic Analysis Of Born-Infeld-like Models In Nonlinear Electrodynamics

Inspired by the extensive applications of the idea of the Born-Infeld theory,ranging from particle physics,superstring theory,and modified gravity theories,in this paper,two important Born-Infeld-like models in nonlinear electrodynamics are studied,which are one-dimensional polynomial model and-dimensional exponential model.For the one-dimensional quadratic polynomial model,the exact number of positive so-lutions is studied by time mapping analysis and mathematical analysis techniques.The-dimensional exponential model is studied in two chapters.First,we consider the exponential model in R~N(≥2).Firstly,the-dimensional exponential quasilinear problem is trans-formed into a one-dimensional Cauchy problem,and then the existence of radial symmetric solutions is studied by using dynamic shooting method.Second,we consider the exponen-tial model in the bounded domainΩ(?)R~N(≥3).Firstly,we modify the-dimensional exponential quasilinear problem.Secondly,variational solutions of the modified problem is constructed on the Nehari manifold.Finally,the existence of nonnegative nontrivial solutions of the exponential model is obtained by using the fixed point theorem.