一类带有临界指数的Schrodinger-Poisson系统非平凡解的存在性

Existence of Nontrivial Solution for a Class of Schrodinger-Poisson System with Critical Exponent

Schrodinger-Poisson系统起源于半导体理论和量子力学模型。本文研究带有临界指数和一般非线性项的Schrodinger-Poisson系统非平凡解的存在性,克服了临界指数项导致空间紧性缺失的困难。首先,运用变分法和山路引理,获得了Schrodinger方程对应的能量泛函的非平凡临界点;然后,结合解的定义,证明了这个非平凡临界点为系统的一个非平凡解。该结果推广并改进了近期带有临界指数的Schrodinger-Poisson系统的相关结果。

Schrodinger-Poisson systems have its origins in semiconductor theory and quantum mechanical models.This paper studies the existence of nontrivial solutions for a class of Schrodinger-Poisson system with critical exponent and general nonlinear term, overcoming the difficulty of space compactness lack caused by critical exponential term.First, the nontrivial critical point of the energy functional corresponding to Schrodinger equation is obtained by the variational method and Mountain Pass Lemma.Then, the nontrivial critical point is proved to be a nontrivial solution for the system by the aid of the definition of the solution.The result has generalized and improved the recent results of Schrodinger-Poisson system with critical exponent.