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

Gongbao LiGao-Feng Zheng — 2006

Revista Matemática Iberoamericana

In this paper, we are concerned with the asymptotically linear elliptic problem -Δu + λu = f(u), u ∈ H (Ω) in an exterior domain Ω = RO (N ≥ 3) with O a smooth bounded and star-shaped open set, and lim f(t)/t = l, 0 < l < +∞. 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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