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	Liouville-type theorems for polyhannonic systems in R-N
	Liu, J ; Guo, YX ; Zhang, YJ
	2006
关键词	Liouville theorem polyharmonic systems moving planes method POSITIVE SOLUTIONS EQUATIONS
英文摘要	In this note, we consider the polyharmonic system (-Delta)(m) u = v(alpha), (-Delta)(m) v = in R-N with N > 2m and alpha >= 1, beta >= 1, where (-Delta)(m) is the polyharmonic operator. For 1/(alpha + 1) + 1/ (beta + 1) > (N - 2m)/N, we prove the non-existence of non-negative, radial, smooth solutions. For 1 < alpha, beta < (N + 2m)/(N - 2m), we show the non-existence of non-negative smooth solutions. In addition, for either (N - 2m)beta < N/alpha + 2m or (N - 2m)alpha < N/beta + 2m with alpha, beta > 1, we show the non-existence of non-negative smooth solutions for polyharmonic system of inequalities (-Delta)(m) u >= v(alpha), (-Delta)(m) v >= mu(beta). More general, we can prove that all the above results hold for the system (-Delta)(m) u = v(alpha), (-Delta)(n) v = 0 in RN with N > max(2m, 2n) and alpha >= 1, beta >= 1. (c) 2005 Elsevier Inc. All rights reserved.; Mathematics; SCI(E); 26; ARTICLE; 2; 685-709; 225
语种	英语
出处	SCI
出版者	微分方程杂志
内容类型	其他
源URL	[http://hdl.handle.net/20.500.11897/252022]
专题	数学科学学院
推荐引用方式 GB/T 7714	Liu, J,Guo, YX,Zhang, YJ. Liouville-type theorems for polyhannonic systems in R-N. 2006-01-01.

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