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

Authors:	Hwai-Chiuan F Wang

Institution:	Department of Mathematics, National Tsing Hua University, Hsinchu, Taiwan

Abstract:	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 in various $\Omega$ . We also show there exist at least two positive solutions of perturbed semilinear elliptic equations in $\Omega$ .

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