Existence of positive entire solutions of a semilinear elliptic problem with a gradient term
β Scribed by Hongtao Xue; Xigao Shao
- Publisher
- Elsevier Science
- Year
- 2009
- Tongue
- English
- Weight
- 426 KB
- Volume
- 71
- Category
- Article
- ISSN
- 0362-546X
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π SIMILAR VOLUMES
We show that entire positive solutions exist for the semilinear elliptic system u = p x v Ξ± , v = q x u Ξ² on R N , N β₯ 3, for positive Ξ± and Ξ², provided that the nonnegative functions p and q are continuous and satisfy appropriate decay conditions at infinity. We also show that entire solutions fail
It is proved that the singular semilinear elliptic equation yβ¬u s p x g u , Ε½ . n Ε½ . 1 Ε½Ε½ . Ε½ .. lim g s s qΟ±, and g g C 0, Ο± , 0, Ο± which is s Βͺ 0 Ε½ . 2qβ£ Ε½ n . strictly decreasing in 0, Ο± , has a unique positive C R solution that decays to l o c Ο± Ε½ . Ε½ . Ε½ . zero near Ο± provided H t t dt -Ο±, w
Ε½ . Ε½ . decays to zero near Ο± provided H t t dt -Ο±, where t s max p x . Fur-0 < x <st thermore, they show that this condition on p is nearly optimal.