A New Theorem on N-th Order Differential Equation with Retarded Argument

Abstract: In this work, using the well-known mean-value theorem (Lagrange's theorem) we obtain an inequality for n-th order differential equations with retarded argument. If the retarded argument vanishes then the inequality turns to an inequality for n-th order ordinary differential equations which plays a vital role in the proof of existence theorem for n-th order ordinary differential equations.