Nonoscillation theorems of second order nonlinear differential equations

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