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

作　　者：GUO ZongMing ZHOU Feng 

机构地区：[1]Department of Mathematics,Henan Normal University [2]Center for PDEs and Department of Mathematics,East China Normal University

出　　处：《Science China Mathematics》2015年第11期2301-2316,共16页中国科学：数学（英文版）

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)

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.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 monotonicity 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.

关 键 词：sub-harmonicity monotonicity formula singular nonlinearity finite Morse index solutions 

分 类 号：O175.25[理学—数学]