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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Positive solutions of nonlinear elliptic equations in the Euclidean plane


Authors: U. Ufuktepe and Z. Zhao
Journal: Proc. Amer. Math. Soc. 126 (1998), 3681-3692
MSC (1991): Primary 60J45, 60J65
MathSciNet review: 1616593
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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 $D$ 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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Additional Information

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

Z. Zhao
Affiliation: Department of Mathematics, University of Missouri, Columbia, Missouri 65211
Email: mathzz@mizzou1.missouri.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-98-04985-5
PII: S 0002-9939(98)04985-5
Received by editor(s): March 10, 1997
Communicated by: Jeffrey B. Rauch
Article copyright: © Copyright 1998 American Mathematical Society