Existence and Asymptotic Behavior of Solutions for Schrödinger-Born-Infeld System in R3 with a General Nonlinearity

Abstract

In this paper, we study the related properties of the solutions of a class of generalized Schrödinger-Born-Infeld system. In contemporary theoretical physics, the Schrödinger-Born-Infeld system also plays an active and important role. The coupling problem between the Schrödinger equation and the logarithmic type Born-Infeld equation gives rise to insights and new ideas about how space-time geometry and matter interactions can be coupled. Our work is to describe the interaction between matter and electromagnetic field from a dualistic viewpoint. We will synthetically apply variational methods, truncation techniques and other analytical tools to establish the existence and asymptotic behavior of solutions for the coupled system under certain conditions. Our studies will unveil a broad spectrum of systems of elliptic equations with logarithmic nonlinearity and rich properties and structures, which present new challenges.