Existence and Nonexistence of Entire Positive Solutions of Semilinear Elliptic Systems |
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Authors: | Xuefeng WangAihua W. Wood |
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Affiliation: | a Department of Mathematics, Tulane University, New Orleans, Louisiana, 70118, f1xdw@math.tulane.eduf1b 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 |
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Abstract: | We show that entire positive solutions exist for the semilinear elliptic system Δu = p(x)vα, Δv = q(x)uβ on RN, 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. |
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Keywords: | entire solution semilinear elliptic system |
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