Yarak, Coskun; Shaw, Michael D. Initial time difference stability in terms of two measures and a variational comparison result. (English) Zbl 1149.34034 Dyn. Contin. Discrete Impuls. Syst., Ser. A, Math. Anal. 15, No. 3, 417-425 (2008). This paper investigates initial time difference stability in terms of two measures and generalized variation of parameter techniques are unified with Lyapunov-like functions to establish a variational comparison result. At the beginning, the definitions necessary for the analysis of the initial time difference stability in terms of two measures are given. Further, a variational comparison result for vector Lyapunov-like functions is presented and applied to establish an initial time difference stability criteria in terms of two measures. An example is presented to illustrate how the results can be applied. Reviewer: Vasile Dragan (Bucureşti) Cited in 9 Documents MSC: 34D23 Global stability of solutions to ordinary differential equations 34D10 Perturbations of ordinary differential equations 34D05 Asymptotic properties of solutions to ordinary differential equations Keywords:initial time difference; Lyapunov-like functions; perturbed differential systems; stability in terms of two measures; variational comparison result PDFBibTeX XMLCite \textit{C. Yarak} and \textit{M. D. Shaw}, Dyn. Contin. Discrete Impuls. Syst., Ser. A, Math. Anal. 15, No. 3, 417--425 (2008; Zbl 1149.34034)