Global behavior of positive solutions of nonlinear three-point boundary value problems

We investigate the structure of the positive solution set for nonlinear three-point boundary value problems of the formu″+h(t)f(u)=0,u(0)=0,u(1)=λu(η),where η∈(0,1) is given, λ∈[0,1η) is a parameter, f∈C([0,∞),[0,∞)) satisfies f(s)>0 for s>0, and h∈C([0,1],[0,∞)) is not identically zero on any subinterval of [0,1]. Our main results demonstrate the existence of continua of positive solutions of the above problem.