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Classical and Weak Solutions of a Singular Semilinear Elliptic Problem

✍ Scribed by Alan V Lair; Aihua W Shaker

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
222 KB
Volume
211
Category
Article
ISSN
0022-247X

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✦ Synopsis

The singular semilinear elliptic equation ⌬ u q p x f u s 0 is shown to have a n Ž . unique positive classical solution in R that decays to zero at

provided f is a non-increasing continuously differentiable function on 0, Ο± . It is also shown that the equation has a unique weak H 1 -solution on a bounded domain 0 β‘€ Ε½ .

Ε½ .

2 provided H f s ds -Ο± and p x g L .

πŸ“œ SIMILAR VOLUMES

Entire Solution of a Singular Semilinear
Entire Solution of a Singular Semilinear Elliptic Problem
✍ Alan V. Lair; Aihua W. Shaker πŸ“‚ Article πŸ“… 1996 πŸ› Elsevier Science 🌐 English βš– 129 KB

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.

A Remark on the Existence of Entire Solu
A Remark on the Existence of Entire Solutions of a Singular Semilinear Elliptic Problem
✍ Zhijun Zhang πŸ“‚ Article πŸ“… 1997 πŸ› Elsevier Science 🌐 English βš– 118 KB

It is proved that the singular semilinear elliptic equation y⌬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 . 2q␣ 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

A Note on Multiple Solutions of Some Sem
A Note on Multiple Solutions of Some Semilinear Elliptic Problems
✍ E.N. Dancer; Yihong Du πŸ“‚ Article πŸ“… 1997 πŸ› Elsevier Science 🌐 English βš– 228 KB

We discuss the existence of multiple solutions of nonlinear elliptic equations by a combination of variational, topological methods and the generalized Conley index theory. We obtain several positive solutions and sign-changing solutions. Our main point is to show the usefulness of the Morse inequal