A nonlocal elliptic equation in a bounded domain

Piotr Fijałkowski; Bogdan  Przeradzki; Robert Stańczy

Piotr Fijałkowski ; Bogdan Przeradzki ; Robert Stańczy

Banach Center Publications, Tome 65 (2004), p. 127-133 / Harvested from The Polish Digital Mathematics Library

Résumé

The existence of a positive solution to the Dirichlet boundary value problem for the second order elliptic equation in divergence form $- \sum_{i, j = 1}^{n} D_{i} (a_{i j} D_{j} u) = f (u, \int_{Ω} g (u^{p}))$ , in a bounded domain Ω in ℝⁿ with some growth assumptions on the nonlinear terms f and g is proved. The method based on the Krasnosel’skiĭ Fixed Point Theorem enables us to find many solutions as well.

Publié le : 2004-01-01

Zbl 1235.35116

EUDML-ID : urn:eudml:doc:281692

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     author = {Piotr Fija\l kowski and Bogdan  Przeradzki and Robert Sta\'nczy},
     title = {A nonlocal elliptic equation in a bounded domain},
     journal = {Banach Center Publications},
     volume = {65},
     year = {2004},
     pages = {127-133},
     zbl = {1235.35116},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc66-0-8}
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Piotr Fijałkowski; Bogdan  Przeradzki; Robert Stańczy. A nonlocal elliptic equation in a bounded domain. Banach Center Publications, Tome 65 (2004) pp. 127-133. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc66-0-8/