Positive solutions of nonlinear elliptic equations in the Euclidean plane
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- by U. Ufuktepe and Z. Zhao PDF
- Proc. Amer. Math. Soc. 126 (1998), 3681-3692 Request permission
Abstract:
In the present paper, we study the existence of solutions to the problem \[ \begin {cases} \Delta u+f(x,u)=0 & \text {in $D$}\\ u>0&\text {in $D$}\\ u=0 & \text {on $\partial D$} \end {cases} \] 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.References
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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
- Received by editor(s): March 10, 1997
- Communicated by: Jeffrey B. Rauch
- © Copyright 1998 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 126 (1998), 3681-3692
- MSC (1991): Primary 60J45, 60J65
- DOI: https://doi.org/10.1090/S0002-9939-98-04985-5
- MathSciNet review: 1616593