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The effect of domain shape on the number of positive and nodal solutions for semilinear elliptic equations

✍ Scribed by Tsung-fang Wu

Publisher
Elsevier Science
Year
2007
Tongue
English
Weight
293 KB
Volume
67
Category
Article
ISSN
0362-546X

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✦ Synopsis

In this paper, we study the effect of domain shape on the number of positive and nodal (sign-changing) solutions for a class of semilinear elliptic equations. We prove a semilinear elliptic equation in a domain Ω that contains m disjoint large enough balls has m 2 2-nodal solutions and m positive solutions.

πŸ“œ SIMILAR VOLUMES

On the Existence of Positive Solutions f
On the Existence of Positive Solutions for Semilinear Elliptic Equations in the Annulus
✍ H.Y. Wang πŸ“‚ Article πŸ“… 1994 πŸ› Elsevier Science 🌐 English βš– 180 KB

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.