Oscillation Theorems for Nonlinear Second Order Forced Differential Equations

Abstract

Relating to the oscillation theory, in the present paper, we consider a class of forced nonlinear differential equations of second order. However, we discuss the problem of finding sufficient criteria for all solutions of these equations to be oscillate. By employing a generalized Ricati technique and also using an integral averaging technique, we derive several new oscillation theorems. Our results obtained here generalize and improve some of well-known ones in the literature. Some carefully selected examples are also given to illustrate the effect of impulses on the oscillatory behavior of all solutions for this class.