Proceedings of the American Mathematical Society

Author(s): U. Ufuktepe; Z. Zhao
Journal: Proc. Amer. Math. Soc. 126 (1998), 3681-3692.
MSC (1991): Primary 60J45, 60J65
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Abstract: In the present paper, we study the existence of solutions to the problem

$\begin{equation*}\left\{ \begin{array}{cc} \Delta u+f(x,u)=0 & \text{in }D u>0&\text{in }D u=0 & \text{on }\partial D\end{array}\right. \end{equation*}$

where

is an unbounded domain in $\mathbb{R}^2$ with a compact nonempty boundary $\partial D$ consisting of finitely many Jordan curves. The goal is to prove an existence theorem for the above problem in a general setting by using Brownian path integration and potential theory.

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Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 60J45, 60J65

U. Ufuktepe
Affiliation: Department of Mathematics, University of Missouri, Columbia, Missouri 65211
Address at time of publication: Akdeniz Universitesi, Fen-Edebiyat Fakultesi, Matematik Bolumu, 07058 Antalya, Turkey
Email: uunal@pascal.sci.akdeniz.edu.tr

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