It is proved that the singular semilinear elliptic equation yโฌu s p x g u , ลฝ . n ลฝ . 1 ลฝลฝ . ลฝ .. lim g s s qฯฑ, and g g C 0, ฯฑ , 0, ฯฑ which is s ยช 0 ลฝ . 2qโฃ ลฝ n . strictly decreasing in 0, ฯฑ , has a unique positive C R solution that decays to l o c ฯฑ ลฝ . ลฝ . ลฝ . zero near ฯฑ provided H t t dt -ฯฑ, w
Entire Solution of a Singular Semilinear Elliptic Problem
โ Scribed by Alan V. Lair; Aihua W. Shaker
- Publisher
- Elsevier Science
- Year
- 1996
- Tongue
- English
- Weight
- 129 KB
- Volume
- 200
- Category
- Article
- ISSN
- 0022-247X
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โฆ Synopsis
ลฝ . ลฝ . decays to zero near ฯฑ provided H t t dt -ฯฑ, where t s max p x . Fur-0 < x <st thermore, they show that this condition on p is nearly optimal.
๐ SIMILAR VOLUMES
The singular semilinear elliptic equation โฌ u q p x f u s 0 is shown to have a n ลฝ . unique positive classical solution in R that decays to zero at provided f is a non-increasing continuously differentiable function on 0, ฯฑ . It is also shown that the equation has a unique weak H 1 -solution on a b
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 โฅ 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