JournalsrmiVol. 22, No. 2pp. 559–590

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

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