论文信息 - Positive solutions of nonlinear three-point boundary-value problems

Positive solutions of nonlinear three-point boundary-value problems

Abstract Let a∈C[0,1], b∈C([0,1],(−∞,0]). Let φ1(t) be the unique solution of the linear boundary value problem u″(t)+a(t)u′(t)+b(t)u(t)=0, t∈(0,1), u(0)=0, u(1)=1. We study the existence of positive solutions to the nonlinear boundary-value problem u″(t)+a(t)u′(t)+b(t)u(t)+h(t)f(u)=0, t∈(0,1), u(0)=0, αu(η)=u(1), where 0 0, and f∈C([0,∞),[0,∞)). We show the existence of at least one positive solution if f is either superlinear or sublinear by applying the fixed point theorem in cones.

Haiyan Wang | Ruyun Ma | Haiyan Wang | Ruyun Ma

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