Exploring Nonoscillatory Solutions in Second-Order Neutral Differential Equations with Distributed Deviating Arguments

The occurrence of oscillation and non-oscillation is common across various models in real-world applications. For instance, impulsive partial neutral differential equations in mathematical biology and biomathematics often display both oscillatory and non-oscillatory solutions. In our investigation, we establish specific criteria that guarantee the presence of non-oscillatory solutions for variable coefficient nonlinear second-order neutral differential equations with distributed deviating arguments and a forcing term. In this work, we obtained an extension of some existing results in the literature. Using the Banach contraction principle, we obtained new sufficient conditions of existence conditions. The proof of positive solutions was provided by showing the existence of a fixed point. At the end of the paper, we give an example showing how we apply one of the theorems we have learnt.