Hyers-Ulam stability criteria for third order nonlinear differential equations with nonlinear damping

Abstract

This paper is concerned with the Hyers-Ulam stability of third order nonlinear differential equations with nonlinear damping. New criteria are developed to transform the ordinary differential equations under consideration to integral inequalities. By employing the Gronwall-Bellman-Bihari type integral inequality, the stability of ordinary differential equations is proved. Moreover, the Hyers-Ulam constants are established. Lastly, the obtained results are not only new but also included the results stated in [14, 17].