Existence and Nonexistence of Entire Positive Solutions of Semilinear Elliptic Systems期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Existence and Nonexistence of Entire Positive Solutions of Semilinear Elliptic Systems

Authors:	Xuefeng WangAihua W Wood

Institution:	^a Department of Mathematics, Tulane University, New Orleans, Louisiana, 70118, f1xdw@math.tulane.eduf1 ^b Department of Mathematics and Statistics, Air Force Institute of Technology/ENC, 2950 P Street, Wright-Patterson Air Force Base, Ohio, 45433-7765, f2Aihua.Wood@afit.af.milf2

Abstract:	We show that entire positive solutions exist for the semilinear elliptic system Δu = p(x)v^α, Δv = q(x)u^β on R^N, N ≥ 3, for positive α and β, provided that the nonnegative functions p and q are continuous and satisfy appropriate decay conditions at infinity. We also show that entire solutions fail to exist if the functions p and q are of slow decay.

Keywords:	entire solution semilinear elliptic system
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