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

Wang, Hwai-Chiuan

doi:10.1090/S0002-9947-00-02456-9

A Palais-Smale approach to problems in Esteban-Lions domains with holes
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by Hwai-Chiuan F. Wang PDF

Trans. Amer. Math. Soc. 352 (2000), 4237-4256 Request permission

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 $(1)$ in various $\Omega$. We also show there exist at least two positive solutions of perturbed semilinear elliptic equations in $\Omega$.

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