Shi, JunpingYao, Miaoxin2021-05-172021-05-172005-01-02Shi, J., & Yao, M. (2005). Positive solutions for elliptic equations with singular nonlinearity. <i>Electronic Journal of Differential Equations, 2005</i>(04), pp. 1-11.1072-6691https://hdl.handle.net/10877/13575We study an elliptic boundary-value problem with singular non-linearity via the method of monotone iteration scheme: -∆u(x) = ƒ(x, u(x)), x ∈ Ω, u(x) = ϕ(x), x ∈ ∂Ω, Where ∆ is the Laplacian operator, Ω is a bounded domain in ℝN, N ≥ 2, ϕ ≥ 0 may take the value 0 on ∂Ω, and ƒ(x, s) is possibly singular near s = 0. We prove the existence and the uniqueness of positive solutions under a set of hypotheses that do not make neither monotonicity nor strict positivity assumption on ƒ(x, s), which improvements of some previous results.Text11 pages1 file (.pdf)enAttribution 4.0 InternationalSingular nonlineararityElliptic equationPositive solutionsMonotonic iterationArticle