ASYMPTOTIC AND OSCILLATORY BEHAVIOR OF DIFFERENTIAL EQUATIONS WITH MULTIPLE DELAYS AND A NONLINEAR NEGATIVE NEUTRAL TERM

This study covers the oscillatory characteristics of solutions of delay differential equations. In order to test the oscillation of all solutions, we establish three distinct criteria and take into account the noncanonical situation. The purpose of establishing various criteria is to achieve a number of benefits in the oscillation test, namely applying the criterion to Euler's equation yields the sharp condition, the influence of delay function of the criterion, and applying to some cases that have not been studied previously. In previous works that treated the studied equation in its general form, only classical criteria were obtained for the canonical case. Finally, we demonstrate that our findings are a generalization and extension of earlier findings in the literature through discussion and examples.