Second-Order Neutral Differential Equations: Improved Criteria for Testing the Oscillation - Osama Moaaz; Ali Muhib; Saud Owyed; Emad E. Mahmoud; Aml Abdelnaser (Journal of Mathematics)
The main purpose of this study is to establish new improved conditions for testing the oscillation of solutions of second-order neutral differential equation rlu′lγ′+qlxβσl=0, where l≥l0 and ul≔xl+pxϱl. By optimizing the commonly used relationship x>1−pu, we obtain new criteria that give sharper results for oscillation than the previous related results. Moreover, we obtain criteria of an iterative nature. Our new results are illustrated by an example.