Positive solutions for elliptic equations with singular nonlinearity
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We 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.
CitationShi, J., & Yao, M. (2005). Positive solutions for elliptic equations with singular nonlinearity. Electronic Journal of Differential Equations, 2005(04), pp. 1-11.
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