New Conditions for Testing the Oscillation of Solutions of Second-Order Nonlinear Differential Equations with Damped Term

Abstract

This paper deals with the oscillatory behavior of solutions of a new class of second-order nonlinear differential equations. In contrast to most of the previous results in the literature, we establish some new criteria that guarantee the oscillation of all solutions of the studied equation without additional restrictions. Our approach improves the standard integral averaging technique to obtain simpler oscillation theorems for new classes of nonlinear differential equations. Two examples are presented to illustrate the importance of our findings.

Second-Order Damped Differential Equations with Superlinear Neutral Term: New Criteria for Oscillation

“…Since Sturm [3] began studying the term oscillation, the researchers have shown remarkable interest in searching for different ways and methods to develop the qualitative theory of functional differential equations as an intermediate tool for transforming realworld phenomena into purely mathematical models that can be dealt with, solved, and studied easily. It is known that the qualitative approach does not seek explicit solutions but is concerned with the behaviour of solutions to differential equations.…”