A nonlocal elliptic equation in
 a bounded domain

Piotr Fijałkowski; Bogdan  Przeradzki; Robert Stańczy

doi:10.4064/bc66-0-8

Instytut Matematyczny Polskiej Akademii Nauk / Institute of Mathematics / Publishing house / Banach Center Publications / All volumes

A nonlocal elliptic equation in a bounded domain

Volume 66 / 2004

Piotr Fijałkowski, Bogdan Przeradzki, Robert Stańczy Banach Center Publications 66 (2004), 127-133 MSC: Primary 35J65. DOI: 10.4064/bc66-0-8

Abstract

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

Authors

Piotr FijałkowskiFaculty of Mathematics, University of Łódź
Banacha 22, 90-238 Łódź, Poland
e-mail
Bogdan PrzeradzkiFaculty of Mathematics, University of Łódź

Banacha 22, 90-238 Łódź, Poland
e-mail
Robert StańczyWydział Matematyki, Uniwersytet Łódzki, ul. Banacha 22, 90-238
Łódź, Poland;
and
Instytut Matematyczny, Uniwersytet Wrocławski,
Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland
e-mail

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