Positive Solutions Of Three-point Boundary Value Problems Of Singular Second Order ODE

In this paper, we investigate three-point boundary value problem of singular second order ordinary differential equation (ODE)where f:(0,1)×[0,∞)→[0,∞) is contionuous.In quasi-homogeneous sublinear case, a necessary and sufficient condition for the existence of C~1 [0,1] positive solution is given using method of lower and upper solutions. We also give a sufficient condition for the existence of C[0,1] positive solution. Meanwhile, a uniqueness result is obtained.Using the fixed point theorem of cone expansion and compression of norm type, we prove the existence of at least one C[0,1] also we get a necessary and sufficient condition for the existence of C~1[0,1] positive solutions in quasi-homogeneous superlinear case. Finally, we discussed the existence of multiple positive solutions.