Existence and uniqueness of positive solutions of semilinear elliptic equations  

作　　者：Qiu-yi DAI Yu-xia FU Yong-geng GU 

机构地区：[1]Department of Mathematics,Hunan Normal University,Changsha 410081,China [2]Department of Applied Mathematics,Hunan University,Changsha 410082,China

出　　处：《Science China Mathematics》2007年第8期1141-1156,共16页中国科学：数学（英文版）

基　　金：the National Natural Science Foundation of China(Grant Nos.10671064,10171029)

摘　　要：This paper is devoted to the study of existence,uniqueness and non-degeneracy of positive solutions of semi-linear elliptic equations.A necessary and sufficient condition for the existence of positive solutions to problems is given.We prove that if the uniqueness and non-degeneracy results are valid for positive solutions of a class of semi-linear elliptic equations,then they are still valid when one perturbs the differential operator a little bit.As consequences,some uniqueness results of positive solutions under the domain perturbation are also obtained.This paper is devoted to the study of existence, uniqueness and non-degeneracy of positive solutions of semi-linear elliptic equations. A necessary and sufficient condition for the existence of positive solutions to problems is given. We prove that if the uniqueness and non-degeneracy results are valid for positive solutions of a class of semi-linear elliptic equations, then they are still valid when one perturbs the differential operator a little bit. As consequences, some uniqueness results of positive solutions under the domain perturbation are also obtained.

关 键 词：semilinear elliptic equation positive solution EXISTENCE UNIQUENESS NONDEGENERACY 35J65 

分 类 号：O175.25[理学—数学]