On the stability of second order parametric ordinary differential equations and applications

This paper investigates the Lipschitz stability for a parametric version of the general second order Ordinary Differential Equation (ODE) initial-value Cauchy problem.Based on a direct computation using Perov's inequality, we first establish a Lipschitz stability result for this problem under a partial variation of the data.Next, we apply our abstract result to second order differential equations governed by cocoercive operators.Then, we discuss more concrete applications of the stability for two specific applied mathematical models inherent in electricity and control theory.Finally, we provide numerical tests based on the software source Scilab, which are done with respect to parametric linear time invariant systems, illustrating the validity of our theoretical results.