Applied Mathematics & Information Sciences

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The objective of this work is to improve the relationships between the solutions of neutral differential equations and their corresponding functions in the classical case. We use these relationships to optimize the conditions that test the oscillation of solutions to Emden-Fowler neutral differential equations. We consider both cases p < 1 and p > 1. In the case p > 1, we test the oscillation of the solutions without imposing the conventional constraints on the delay functions. The approach adopted depends on deducing new properties for the positive solutions of the studied equation, and these properties are of an iterative nature. The iterative nature of properties helps to create relationships and conditions that can be used more than once. By applying the results to special cases of the studied equation, we can clarify the importance of the new results and compare them with the relevant previous results.

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