Positive solutions for elliptic equations with singular nonlinearity.
Junping Shi, Miaoxin Yao · 2005
In this paper, a nonlinear elliptic boundary value problem with singular nonlinearity Lu(x) = f(x, u(x)), x ∈ Ω, u(x) = φ(x), x ∈ ∂Ω, is studied, where L is a uniformly elliptic operator, Ω is a bounded domain in RN, N ≥ 2, φ ≥ 0 may take the value 0 on ∂Ω, and f(x, s) is possibly singular near s = 0. Some results regarding the existence of positive solutions for the problem are given under a set of hypotheses that make neither monotonicity nor strict positivity assumption on f(x, s), and they are improvements of some previous results on this subject. Also, a uniqueness criterion is given. 1 The running head of the paper: Singular elliptic equations