On the stability in variation of non-autonomous differential equations with perturbations
In this paper, the authors investigate the problem of stability in variation of solutions for nonautonomous differential equations of the form \N\[\N\dot x=f(t,x),\tag{1}\N\]\Nwhere \(f: \mathbb{R}^+\times \mathbb{R}^n\to\mathbb{R}^n\), is a continuous function and locally Lipschitz with respect to \(x\) such that \(f(t, 0) = 0\), \(t > 0\) is time. Some new sufficient conditions for the asymptotic or exponential stability for the zero solution of system (1) are presented by using Lyapunov functions that are not necessarily smooth. The proposed approach for stability analysis is based on the determination of the bounds that characterize the asymptotic convergence of the solutions to a certain closed set containing the origin. Some illustrative examples are given to prove the validity of the main results.
scientific article; zbMATH DE number 7879978
scientific article