Ulam stability of perturbed third-order nonlinear differential equations

Abstract

This paper investigates the Hyers-Ulam stability of two classes of perturbed third-order nonlinear differential equations. Using the Cauchy formula for repeated integrals, the mean value theorem for integrals, and nonlinear Gronwall-Bellman-Bihari type inequalities, we establish sufficient conditions for Hyers-Ulam stability and derive explicit formulas for the corresponding stability constants. The existence and uniqueness of solutions are established under appropriate Lipschitz conditions. Several special cases, including the homogeneous case, are analyzed. Illustrative examples are provided to demonstrate the applicability of our theoretical results.