Geodesic
Uniqueness for a semilinear elliptic equation in non-contractible domains under supercritical growth conditions
Electronic Journal of Differential Equations, Tome 1999 (1999).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We apply the Pohozaev identity to sub-domains of a tubular neighbourhood of a closed or broken curve in $\Bbb R^n$ and establish uniqueness results for the smooth solutions of the Dirichlet problem for $-\Delta u+|u|^{p-1}u=0$. We require the domain to be in $\Bbb R^n$ with $n \geq 4$ and with $p greater than (n+1)/(n-3)$.
Classification : 35J65, 35B05, 58E05
Keywords: semilinear elliptic equation, supercritical growth, uniqueness, non-contractible domains, pohozaev identity 
@article{EJDE_1999__1999__a89,
     author = {Zhang, Kewei},
     title = {Uniqueness for a semilinear elliptic equation in non-contractible domains under supercritical growth conditions},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {1999},
     year = {1999},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_1999__1999__a89/}
}
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Zhang, Kewei. Uniqueness for a semilinear elliptic equation in non-contractible domains under supercritical growth conditions. Electronic Journal of Differential Equations, Tome 1999 (1999). http://geodesic.mathdoc.fr/item/EJDE_1999__1999__a89/