E-resources
Peer reviewed
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Zhang, Zhijun; Cheng, Jiangang
Nonlinear analysis, 05/2004, Volume: 57, Issue: 3Journal Article
By applying the properties of the unique classical solution to the singular boundary value problem on half line − p″( s)= g( p( s)), p( s)>0, s∈(0,∞), p(0)=0,lim s→∞ p′( s)= b⩾0, and constructing the new comparison functions, they show the existence and the optimal global estimates of solutions to singular nonlinear Dirichlet problems − Δu=k(x)g(u),u>0,x∈Ω,u| ∂Ω=0 , where Ω is a bounded domain with smooth boundary in R N ; g( s) is nonincreasing and positive in (0, ∞), ∫ 1 ∞ g(t) dt<∞ and lim s→0 + g(s)=+∞;k∈C α(Ω) is positive in Ω, and may be singular or zero on the boundary.
