二维具临界指数增长的椭圆方程基态解的存在性

Ground State Solutions for Elliptic Equations with Critical Exponential Growth in R

本文利用临界点理论研究半线性Schrodinger方程{u=0,x∈Ωσ -△u=f(x,u),x∈Ω这里,Ω是R^(2)中的有界区域,f(x,u):Ω×R满足Trudinger-Moser不等式意义下的临界指数增长.通过对极小极大水平值进行精细估计,结合非Nehari流形方法和Trudinger-Moser不等式,获得了以上问题存在Nehari型基态解以及非平凡解的结果,改进了已有文献中的相应结果.

In this paper,we study the existence of solutions for the following semi-linear Schrodinger equations with critical exponential growth,{u=0,x∈Ωσ -△u=f(x,u),x∈Ωhere,Ω∈R^(2)is a bounded domain with smooth boundary.Through combining a more precise estimation about the minimax level with non-Nehari manifold method and TrudingerMoser inequality,we obtain the existence results of nontrivial solutions and Nehari-type ground state solution for the above equation.Our results improve and extend the existing results.