Positive solutions for elliptic equations with singular nonlinearity
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Date
2005-01-02
Authors
Shi, Junping
Yao, Miaoxin
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University-San Marcos, Department of Mathematics
Abstract
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.
Description
Keywords
Singular nonlineararity, Elliptic equation, Positive solutions, Monotonic iteration
Citation
Shi, J., & Yao, M. (2005). Positive solutions for elliptic equations with singular nonlinearity. <i>Electronic Journal of Differential Equations, 2005</i>(04), pp. 1-11.
Rights
Attribution 4.0 International