Multiplicity of positive solutions for second-order three-point boundary value problems

We study the multiplicity of positive solutions for the second-order three-point boundary value problem u″+λh(t)f(u)=0, t (0,1), u(0)=0, αu(η)=u(1) where η: 0 < η < 1, 0 < α < 1/η. The methods employed are fixed-point index theorems and Leray-Schauder degree and upper and lower solutions.