On the oscillation criteria for neutral differential equations with several delays

In this research, we investigate the oscillatory characteristics and asymptotic behavior of second-order neutral differential equations with various delays, which include both superlinear and sublinear terms. We concentrate in particular on the non-canonical form of these equations. The classic Riccati methodology, which employs multiple replacements, is utilized to simplify and analyze the equations. Using this methodology, we create particular criteria that ensure the oscillation of solutions in the context of nonlinear equations with numerous delays. This study is a significant contribution to the scientific literature since it introduces new approaches to understanding complex dynamical systems affected by time delays. We also include two examples to show how the obtained results can be applied to real scenarios, which enhances the reader's understanding of the methodology and results.