Nonoscillation Theorems of Second Order Nonlinear Differential Equations

<正> The main purpose of this paper is to study the existence of nonoscillatory solutionsof the second order non-linear differential equation (1). The author first generalizes a Wintner'slemma [1,8] to nonlinear equations (i.e. the following Theorem 1 and 4), and then obtains thenecessary and sufficient conditions for the existence of nonoscillatory solutions of (1). These the-orems generalize the corresponding results of [1] to include nonlinear equations. Using the aboveresults, the author further obtains a series of criterion theorems for the existence of nonoscillatorysolutions and comparison theorems for the oscillation and nonoscillation of nonlinear equations.