Existence and Nonexistence of Entire Positive Solutions of Semilinear Elliptic Systems

✍ Scribed by Xuefeng Wang; Aihua W. Wood

• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 80 KB
• Volume: 267
• Category: Article
• ISSN: 0022-247X
• DOI: 10.1006/jmaa.2001.7784

✦ Synopsis

We show that entire positive solutions exist for the semilinear elliptic system u = p x v α , v = 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.  2002 Elsevier Science (USA)