Hyers-Ulam Stability Criteria of Nonlinear Second Order Differential Equations with Nonlinear Damping Terms

Abstract

This work examines the Hyers-Ulam stability criteria for second order nonlinear differential equations of nonlinear damping terms. A key component of our findings is the conversion of all second order nonlinear differential equations considered using criteria developed into integral inequalities for Gronwall-Bellman-Bihari integral inequality to be easily applied. The results obtained extend all the known findings on the stability for second order nonlinear differential equations in the literature. We provide examples to support the validity of our theorems.