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September, 2006 The existence of positive solution to some asymptotically linear elliptic equations in exterior domains
Gongbao Li , Gao-Feng Zheng
Rev. Mat. Iberoamericana 22(2): 559-590 (September, 2006).

Abstract

In this paper, we are concerned with the asymptotically linear elliptic problem $-\Delta u+ \lambda_{0}u=f(u), u\in H_{0}^{1}(\Omega ) $ in an exterior domain $\Omega= \mathbb{R}^{N}\setminus\overline{\mathcal{O}} \left( N\geqslant 3\right) $ with $\mathcal{O}$ a smooth bounded and star-shaped open set, and $\lim_{t\rightarrow +\infty }\frac{ f(t)}{t}=l$, $0<l<+\infty$. Using a precise deformation lemma and algebraic topology argument, we prove under our assumptions that the problem possesses at least one positive solution.

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Gongbao Li . Gao-Feng Zheng . "The existence of positive solution to some asymptotically linear elliptic equations in exterior domains." Rev. Mat. Iberoamericana 22 (2) 559 - 590, September, 2006.

Information

Published: September, 2006
First available in Project Euclid: 26 October 2006

zbMATH: 1134.35038
MathSciNet: MR2294790

Subjects:
Primary: 35J20 , 35J25 , 35J65

Keywords: algebraic topology argument , asymptotically linear elliptic , exterior domain , positive solution

Rights: Copyright © 2006 Departamento de Matemáticas, Universidad Autónoma de Madrid

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Vol.22 • No. 2 • September, 2006
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