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Transactions of the American Mathematical Society

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A Palais-Smale approach to problems in Esteban-Lions domains with holes

Author: Hwai-Chiuan F. Wang
Journal: Trans. Amer. Math. Soc. 352 (2000), 4237-4256
MSC (1991): Primary 35J20, 35J25
Published electronically: March 16, 2000
MathSciNet review: 1650050
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Let $\Omega \subset {\mathbb{R} }^{N}$ be the upper half strip with a hole. In this paper, we show there exists a positive higher energy solution of semilinear elliptic equations in $\Omega $ and describe the dynamic systems of solutions of equation $(1)$ in various $\Omega $. We also show there exist at least two positive solutions of perturbed semilinear elliptic equations in $\Omega $.

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Additional Information

Hwai-Chiuan F. Wang
Affiliation: Department of Mathematics, National Tsing Hua University, Hsinchu, Taiwan

Received by editor(s): July 1, 1996
Received by editor(s) in revised form: May 7, 1998
Published electronically: March 16, 2000
Article copyright: © Copyright 2000 American Mathematical Society

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