In this paper, we are concerned with the asymptotically linear elliptic problem in an exterior domain with a smooth bounded and star-shaped open set, and , . 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. 559–590DOI 10.4171/RMI/466