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

  • Gongbao Li

    Huazhong Normal University, Wuhan, China
  • Gao-Feng Zheng

    Huazhong Normal University, Wuhan, China

Abstract

In this paper, we are concerned with the asymptotically linear elliptic problem Δu+λ0u=f(u),uH01(Ω)-\Delta u+ \lambda_{0}u=f(u), u\in H_{0}^{1}(\Omega ) in an exterior domain Ω=RNO(N3)\Omega= \mathbb{R}^{N}\setminus\overline{\mathcal{O}} \left( N\geqslant 3\right) with O\mathcal{O} a smooth bounded and star-shaped open set, and limt+f(t)t=l\lim_{t\rightarrow +\infty }\frac{ f(t)}{t}=l, 0<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.

Cite this article

Gongbao Li, Gao-Feng Zheng, The existence of positive solution to some asymptotically linear elliptic equations in exterior domains. Rev. Mat. Iberoam. 22 (2006), no. 2, pp. 559–590

DOI 10.4171/RMI/466