Averaging Techniques in The Oscillations of Nonlinear Differential Equations With Alternating Coefficients

Abstract

This paper is concerned with the oscillation theory of a class of second order nonlinear differential equations. Several sufficient conditions for the oscillation of all solutions are established. By using the average property of the integrals of the alternating coefficients as well as the Riccati transformation many oscillatory theorems are proved. However, and as it will be explained, the obtained results here generalize and improve some previous results in the literature. An example is provided to show the applicability of the obtained results.