Geodesic
Bifurcation for some semilinear elliptic equations when the linearization has no eigenvalues
Commentationes Mathematicae Universitatis Carolinae, Tome 34 (1993) no. 1, pp. 125-138
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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 $L^p$ $(2\leq p\leq \infty )$.
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 
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     author = {Rother, Wolfgang},
     title = {Bifurcation for some semilinear elliptic equations when the linearization has no eigenvalues},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {125--138},
     year = {1993},
     volume = {34},
     number = {1},
     mrnumber = {1240210},
     zbl = {0791.35094},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_1993_34_1_a12/}
}
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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/