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Sub-harmonicity,monotonicity formula and finite Morse index solutions of an elliptic equation with negative exponent 被引量：3

Sub-harmonicity,monotonicity formula and finite Morse index solutions of an elliptic equation with negative exponent
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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.
作者 GUO ZongMing ZHOU Feng
机构地区 Department of Mathematics Center for PDEs and Department of Mathematics
出处 《Science China Mathematics》 SCIE CSCD 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)
关键词 sub-harmonicity monotonicity formula singular nonlinearity finite Morse index solutions Morse指标 椭圆型方程 单调性 调和性 负指数 公式 半线性椭圆方程 指数方程
分类号 O175.25 [理学—基础数学]
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参考文献15

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Science China Mathematics
2015年 第11期

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