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Nonexistence of positive entire solutions for a class of -Laplacian elliptic systems

โœ Scribed by Caisheng Chen; Lanfang Shi; Shenglan Zhu

Publisher
Elsevier Science
Year
2011
Tongue
English
Weight
230 KB
Volume
24
Category
Article
ISSN
0893-9659

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โœฆ Synopsis

In this work we consider the nonexistence of a positive entire solution for the quasilinear elliptic system

where p, q > 1 and ฮฑ > q -1, ฮฒ > p -1. We study the effect of the asymptotic behavior of f (x), g(x) and solutions at infinity on the nonexistence of a positive solution for Problem (0.1). Some sufficient conditions for nonexistence are obtained.

๐Ÿ“œ SIMILAR VOLUMES

Existence and Nonexistence of Entire Pos
Existence and Nonexistence of Entire Positive Solutions of Semilinear Elliptic Systems
โœ Xuefeng Wang; Aihua W. Wood ๐Ÿ“‚ Article ๐Ÿ“… 2002 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 80 KB

We show that entire positive solutions exist for the semilinear elliptic system u = p x v ฮฑ , v = q x u ฮฒ on R N , N โ‰ฅ 3, for positive ฮฑ and ฮฒ, provided that the nonnegative functions p and q are continuous and satisfy appropriate decay conditions at infinity. We also show that entire solutions fail

Three solutions for a class of quasiline
Three solutions for a class of quasilinear elliptic systems involving the -Laplacian
โœ Chun Li; Chun-Lei Tang ๐Ÿ“‚ Article ๐Ÿ“… 2008 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 254 KB

The existence of at least three weak solutions is established for a class of quasilinear elliptic systems involving the ( p, q)-Laplacian with Dirichlet boundary condition. Our technical approach is based on the three-critical-points theorem obtained by B. Ricceri.