POSITIVE SOLUTIONS OF THREE-POINT BOUNDARY VALUE PROBLEM FOR SECOND ORDER DIFFERENTIAL EQUATIONS WITH AN ADVANCED ARGUMENT

摘要

By using the Krasnoselskii's fixed point theorem for cones, conditions for the existence of positive solutions to the three-point boundary value problem for second order differential equation with an advanced argument u″(t) + λa(t)f(u(h(t))) = 0, t ∈ (0,1), u(0) = 0, αu(η) = u(1), where 0<η<1,0<α<1/η and t≤h(t)≤1 are obtained.