Sub-harmonicity,monotonicity formula and finite Morse index solutions of an elliptic equation with negative exponent

作     者：GUO ZongMing ZHOU Feng 

作者机构：Department of MathematicsHenan Normal University Center for PDEs and Department of MathematicsEast China Normal University 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2015年第58卷第11期

页      面：2301-2316页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：supported by National Natural Science Foundation of China(Grant Nos.11171092 and 11271133) Innovation Scientists and Technicians Troop Construction Projects of Henan Province(Grant No.114200510011) 

主　　题：sub-harmonicity monotonicity formula singular nonlinearity finite Morse index solutions 

摘      要：A monotonicity formula for stable solutions to a class of weighted semilinear elliptic equations with ＂negative exponent＂ is established. It is well known that such a monotonieity formula plays an essential role in the study of finite Morse index solutions of equations with ＂positive exponent＂. Unlike the positive exponent case, we will see that both the monotonicity formula and the sub-harmonicity play crucial roles in classifying positive finite Morse index solutions to the equations with negative exponent and obtaining sharp results for their asymptotic behaviors.