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Positive solutions of nonlinear three-point boundary-value problems

2003; Elsevier BV; Volume: 279; Issue: 1 Linguagem: Inglês

10.1016/s0022-247x(02)00661-3

1096-0813

Ruyun Ma, Haiyan Wang,

Differential Equations and Numerical Methods

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<η<1 and 0<αφ1(η) 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.