Positive solutions for three-point boundary value problems with dependence on the first order derivative

AbstractA new fixed point theorem in a cone is applied to obtain the existence of at least one positive solution for the second order three-point boundary value problem x″+f(t,x,x′)=0,0<t<1,x(0)=0,x(1)=αx(η), where f is a nonnegative continuous function, α>0, η∈(0,1), αη