一类临界Schr?dinger方程的正基态径向解

Positive Ground State Radial Solutions for a Class of Critical Schr?dinger Equation

研究了径向空间中带有Sobolev临界指数的Schrodinger方程,不要求方程临界项带有的位势满足周期或渐近周期的相关条件.主要利用Nehari流形和Ekeland变分原理找到相应流形上的极小化序列,进而证明基态径向解的存在性.最后运用强极大值原理证明方程的解是正解,从而得到方程的正基态径向解.

In this paper, a Schroinger equation with critical Sobolev exponent in the radial space has been studied, and the potential of critical term is not periodic or asymptotic periodic. Nehari manifold and Ekeland’s variational principle have been applied to find a sequence of minimizing sequence, moreover, the existence of ground state solutions has been proved. Finally, strong maximum principle implies the solution is positive. Therefore, the existence of a positive ground state radial solution is established.