Oscillatory Behavior of Semi-canonical Nonlinear Neutral Differential Equations of Third-Order Via Comparison Principles

We are dealing here with the oscillatory behaviors of all solutions to a class of semicanonical third-order nonlinear functional differential equations involving both retarded and advanced type deviating arguments in the neutral term. Our main tool is to show that, under certain conditions, a semicanonical equation can be written as an equivalent equation in canonical form. The results presented in this paper are novel even when the studied equation is linear. We also provide several examples to demonstrate the applicability and versatility of our results.