Revista Matemática Iberoamericana


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Volume 22, Issue 2, 2006, pp. 559–590
DOI: 10.4171/RMI/466

Published online: 2006-08-31

The existence of positive solution to some asymptotically linear elliptic equations in exterior domains

Gongbao Li[1] and Gao-Feng Zheng[2]

(1) Huazhong Normal University, Wuhan, China
(2) Huazhong Normal University, Wuhan, China

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

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

Li Gongbao, Zheng Gao-Feng: The existence of positive solution to some asymptotically linear elliptic equations in exterior domains. Rev. Mat. Iberoamericana 22 (2006), 559-590. doi: 10.4171/RMI/466