Comparison theorems on the oscillation of third-order functional differential equations with mixed deviating arguments in neutral term

Abstract

. This study purposes to present some new comparison theorems that guarantee the oscillation of all solutions of third-order functional differential equations with mixed neutral term i.e., the neutral term contains both retarded and advanced arguments. The obtained results are based on comparisons with associated fi rst-order delay differential inequalities and fi rst-order delay differential equations, and they are applicable to both cases where the neutral coef fi cients of differential equation are unbounded and/or bounded. Illustrative examples are also provided to validate the main results.