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 $L^p$ $(2\leq p\leq \infty )$.
@article{118562,
author = {Wolfgang Rother},
title = {Bifurcation for some semilinear elliptic equations when the linearization has no eigenvalues},
journal = {Commentationes Mathematicae Universitatis Carolinae},
volume = {34},
year = {1993},
pages = {125-138},
zbl = {0791.35094},
mrnumber = {1240210},
language = {en},
url = {http://dml.mathdoc.fr/item/118562}
}
Rother, Wolfgang. Bifurcation for some semilinear elliptic equations when the linearization has no eigenvalues. Commentationes Mathematicae Universitatis Carolinae, Tome 34 (1993) pp. 125-138. http://gdmltest.u-ga.fr/item/118562/
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