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

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