Abstract
This paper establishes new oscillation criteria for odd-order half-linear differential equations with retarded arguments in the non-canonical case. By employing a linearization technique, the problem is reduced to studying an associated linear equation, allowing us to analyze oscillatory behavior via comparison with first-order delay differential equations whose properties are well known. The obtained results generalize, improve, and consolidate several existing criteria in the literature. Examples are included to illustrate the practical utility and effectiveness of the proposed method.