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Title: Bifurcation for some semilinear elliptic equations when the linearization has no eigenvalues (English)
Author: Rother, Wolfgang
Language: English
Journal: Commentationes Mathematicae Universitatis Carolinae
ISSN: 0010-2628 (print)
ISSN: 1213-7243 (online)
Volume: 34
Issue: 1
Year: 1993
Pages: 125-138
Category: math
Summary: We prove existence and bifurcation results for a semilinear eigenvalue problem in $\Bbb R^N$ $(N\geq 2)$, where the linearization --- $\vartriangle $ has no eigenvalues. In particular, we show that under rather weak assumptions on the coefficients $\lambda =0$ is a bifurcation point for this problem in $H^1, H^2$ and $L^p$ $(2\leq p\leq \infty )$. (English)
Keyword: bifurcation point
Keyword: variational method
Keyword: eigenvalues
Keyword: exponential decay
Keyword: standing waves
MSC: 35A30
MSC: 35B32
MSC: 35J60
MSC: 35P30
MSC: 35Q40
idZBL: Zbl 0791.35094
idMR: MR1240210
Date available: 2009-01-08T18:01:43Z
Last updated: 2012-04-30
Stable URL:
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