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Entire Solution of a Singular Semilinear Elliptic Problem

โœ 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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โœฆ 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.


๐Ÿ“œ SIMILAR VOLUMES


A Remark on the Existence of Entire Solu
โœ Zhijun Zhang ๐Ÿ“‚ Article ๐Ÿ“… 1997 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 118 KB

It is proved that the singular semilinear elliptic equation yโŒฌu 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 . 2qโฃ 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

Classical and Weak Solutions of a Singul
โœ Alan V Lair; Aihua W Shaker ๐Ÿ“‚ Article ๐Ÿ“… 1997 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 222 KB

The singular semilinear elliptic equation โŒฌ 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

Existence and Nonexistence of Entire Pos
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