A Positive Operator Approach to the Neumann Problem for a Second Order Ordinary Differential EquationU

In this paper the solvability of the second order Neumann problem uY t. qcuX t. qf t, u t..s0, uX 0. sA, uX R. sB. is studied. We suppose that there is a lower solution g and an upper solution b in the reversed order, and we obtain optimal conditions in f to assure the existence of a solution lying between b and g .