摘要
In this paper,we study the Dirichlet problem for a class of semi-linear infinitely degenerate elliptic equations with singular potential term.By using the logarithmic Sobolev inequality and Hardy's inequality,the existence and regularity of multiple nontrivial solutions have been proved.
In this paper, we study the Dirichlet problem for a class of semi-linear infinitely degenerate elliptic equations with singular potential term. By using the logarithmic Sobolev inequality and Hardy＇s inequality, the existence and regularity of multiple nontrivial solutions have been proved.
基金
supported by National Natural Science Foundation of China (Grant No.11131005)
PHD Programs Foundation of Ministry of Education of China (Grant No. 20090141110003)
the Fundamental Research Funds for the Central Universities (Grant No. 2012201020202)
