本项目主要研究非线性Schrodinger方程分别与Bopp-Podolsky电磁理论和Born-Infeld电磁理论的耦合系统，它与电动力学、超弦理论、膜理论和宇宙学等研究有密切的关系，由这些非线性科学问题引出的变分问题属于非线性分析的热点课题。本项目计划在变分框架下通过多种非线性分析方法研究：Schrodinger-Bopp-Podolsky系统变号解的存在性和多解性，以及其临界指数问题基态解的存在性；Schrodinger-Born-Infeld系统解的存在性，非存在性和多解性；解的渐近行为。由于耦合项的非齐次性，以至于很多标准的变分方法和分析技巧不能直接应用。此外，非线性项缺乏（AR）条件使得问题的研究更加复杂。这些困难的解决需要我们进一步发展出新的思想和方法，同时也将促进非线性分析理论与应用的发展。

This project is mainly concerned with nonlinear Schrodinger equation coupled with Bopp-Podolsky electromagnetic theory and Born-Infeld electromagnetic theory respectively, which are related to electrodynamics, superstrings, membranes and cosmology. Variational problems arise in these nonlinear science have become the hot topics in the study of nonlinear analysis. Under the variational structure, we wish to investigate the following problems via several methods in nonlinear analysis: the existence and multiplicity of sign-changing solutions for the Schrodinger-Bopp-Podolsky system, and the existene of ground state solutions for this system involves critical exponent; the existence, nonexistence and multiplicity of solutions for Schrodinger-Born-Infeld system. Moreover, we study the asymptotic behavior of these solutions. Because the coupled terms are nonhomogeneous, many standard variational methods and analysis techniques can't be applied directly. Moreover, it seems much complicated when people try to deal with the lack of (AR) condition for the nonlinearities. To attack these difficulties, we have to develop some new ideas and methods, and the development of theories and applications in nonlinear analysis can be promoted at the same time.