On the Existence of Positive Solutions for Semilinear Elliptic Equations in the Annulus
โ Scribed by H.Y. Wang
- Publisher
- Elsevier Science
- Year
- 1994
- Tongue
- English
- Weight
- 180 KB
- Volume
- 109
- Category
- Article
- ISSN
- 0022-0396
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โฆ Synopsis
We study the existence of positive radial solutions of (A u+g(|x|) f(u)=0) in annuli with Dirichlet (Dirichlet/Neumann) boundary conditions. We prove that the problems have positive radial solutions on any annulus if (f) is sublinear at 0 and (\infty . \quad C 1994) Academic Press, Inc.
๐ SIMILAR VOLUMES
We consider a semilinear elliptic equation, 2u+u p =0 on 0 R #[x # R n |R&1< |x|2. We prove that, when the space dimension n is three, the number of nonequivalent nonradial positive solutions of the equation goes to as R ร . The same result has been known for n=2 and n 4; in those cases, the result
The existence and multiplicity results are obtained for solutions of a class of the Dirichlet problem for semilinear elliptic equations by the least action principle and the minimax methods, respectively.