Positive solutions for second-order three-point boundary value problems

Abstract We establish the existence of positive solutions for the three-point boundary value problem u″ + a(t)f(u)= 0, u(0)=0,u(1) − αu(ν)=b, where b, α > 0, η ∈ (0,1), αη b ∗ such that the problem has at least one solution for 0 ∗ and no solution for b > b ∗ .