Positive Solutions Of Singular Boundary Value Problem Of Fourth ODE

In this paper, we investigate singular boundary value problem of fourth order differential equation (ODE)where f : (0,1) × [0, ∞) → [0, ∞) is continuous.In sublinear case,a necessary and sufficient condition for the existence of C2[0,1] and C3[0,1] positive solution is given using method of lower and upper solutions. We also give a sufficient condition for the existence of C1[0, 1] positive solutions. Meanwhile , some uniqueness results are obtained .Using the fixed point theorem of cone expansion and compression of norm type ,we provide for the existence of at least one C1[0,1], C2[0,1], C3[0,1] positive solutions in superlinear case.Finally ,we discussed the existence of multiple positive solutions .