Non-local elliptic problem in higher dimension
Miyasita, Tosiya
Osaka J. Math., Tome 44 (2007) no. 1, p. 159-172 / Harvested from Project Euclid
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Non-local elliptic problem, $-\Delta v = \lambda \bigl(e^{v}\big/\bigl(\int_{\Omega}e^{v} dx \bigr)^{p}\bigr)$ with Dirichlet boundary condition is considered on $n$-dimensional bounded domain $\Omega$ with $n \geq 3$ for $p>0$. If $\Omega$ is the unit ball, $3 \leq n \leq 9$ and $2/n \leq p \leq 1$, we have infinitely many bendings in $\lambda$ of the solution set in $\lambda-v$ plane. Finally if $\Omega$ is an annulus domain and $p \geq 1$, we show that a solution exists for all $\lambda>0$.
Publié le : 2007-03-14
Classification:  35J60,  35J20,  35P30 
@article{1174324329,
     author = {Miyasita, Tosiya},
     title = {Non-local elliptic problem in higher dimension},
     journal = {Osaka J. Math.},
     volume = {44},
     number = {1},
     year = {2007},
     pages = { 159-172},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1174324329}
}

Miyasita, Tosiya. Non-local elliptic problem in higher dimension. Osaka J. Math., Tome 44 (2007) no. 1, pp.  159-172. http://gdmltest.u-ga.fr/item/1174324329/