Non-local Gel'fand problem in higher dimensions

Tosiya Miyasita; Takashi Suzuki

Banach Center Publications, Tome 65 (2004), p. 221-235 / Harvested from The Polish Digital Mathematics Library

Résumé

The non-local Gel’fand problem, $Δ v + λ e^{v} / \int_{Ω} e^{v} d x = 0$ with Dirichlet boundary condition, is studied on an n-dimensional bounded domain Ω. If it is star-shaped, then we have an upper bound of λ for the existence of the solution. We also have infinitely many bendings in λ of the connected component of the solution set in λ,v if Ω is a ball and 3 ≤ n ≤ 9.

Publié le : 2004-01-01

Zbl 1235.35119

EUDML-ID : urn:eudml:doc:281927

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     author = {Tosiya Miyasita and Takashi Suzuki},
     title = {Non-local Gel'fand problem in higher dimensions},
     journal = {Banach Center Publications},
     volume = {65},
     year = {2004},
     pages = {221-235},
     zbl = {1235.35119},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc66-0-15}
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Tosiya Miyasita; Takashi Suzuki. Non-local Gel'fand problem in higher dimensions. Banach Center Publications, Tome 65 (2004) pp. 221-235. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc66-0-15/