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2002 Multiple solutions of {$H$}-systems on some multiply-connected domains
Futoshi Takahashi
Adv. Differential Equations 7(3): 365-384 (2002). DOI: 10.57262/ade/1356651830

Abstract

In this note, we consider the following problem: \begin{eqnarray*} \left \{ \begin{array}{l} {\Delta} u = 2 u_x \wedge u_y \quad \mbox{in} \; \Omega, \quad u \in {H_0^1(\Omega ; {\bf R}^3)}, \\ u |_{\partial \Omega} = 0, \end{array} \right. \end{eqnarray*} where $\Omega \subset {\bf R}^2$ is a smooth bounded domain. We show that if the domain $\Omega$ is conformal equivalent to a $(K+1)$-ply connected domain satisfying some conditions, then the problem has at least $K$ distinct non-trivial solutions.

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Futoshi Takahashi. "Multiple solutions of {$H$}-systems on some multiply-connected domains." Adv. Differential Equations 7 (3) 365 - 384, 2002. https://doi.org/10.57262/ade/1356651830

Information

Published: 2002
First available in Project Euclid: 27 December 2012

zbMATH: 1126.35325
MathSciNet: MR1867692
Digital Object Identifier: 10.57262/ade/1356651830

Subjects:
Primary: 35J65
Secondary: 35J20 , 35J50 , 35J60 , 58E12

Rights: Copyright © 2002 Khayyam Publishing, Inc.

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Vol.7 • No. 3 • 2002
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