Bifurcation for some semilinear elliptic equations when the linearization has no eigenvalues
Commentationes Mathematicae Universitatis Carolinae, Tome 34 (1993) no. 1, pp. 125-138.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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 $L^p$ $(2\leq p\leq \infty )$.
Classification : 35A30, 35B32, 35J60, 35P30, 35Q40
Keywords: bifurcation point; variational method; eigenvalues; exponential decay; standing waves
@article{CMUC_1993__34_1_a12,
     author = {Rother, Wolfgang},
     title = {Bifurcation for some semilinear elliptic equations when the linearization has no eigenvalues},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {125--138},
     publisher = {mathdoc},
     volume = {34},
     number = {1},
     year = {1993},
     mrnumber = {1240210},
     zbl = {0791.35094},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_1993__34_1_a12/}
}
TY  - JOUR
AU  - Rother, Wolfgang
TI  - Bifurcation for some semilinear elliptic equations when the linearization has no eigenvalues
JO  - Commentationes Mathematicae Universitatis Carolinae
PY  - 1993
SP  - 125
EP  - 138
VL  - 34
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CMUC_1993__34_1_a12/
LA  - en
ID  - CMUC_1993__34_1_a12
ER  - 
%0 Journal Article
%A Rother, Wolfgang
%T Bifurcation for some semilinear elliptic equations when the linearization has no eigenvalues
%J Commentationes Mathematicae Universitatis Carolinae
%D 1993
%P 125-138
%V 34
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CMUC_1993__34_1_a12/
%G en
%F CMUC_1993__34_1_a12
Rother, Wolfgang. Bifurcation for some semilinear elliptic equations when the linearization has no eigenvalues. Commentationes Mathematicae Universitatis Carolinae, Tome 34 (1993) no. 1, pp. 125-138. http://geodesic.mathdoc.fr/item/CMUC_1993__34_1_a12/