Abstract:By employing vector Lyapunov-like functions and the theory of systems of differential inequalities, a variational comparison theorem and generalized variation of constants formula are developed. Furthermore, the usefulness of the variational comparison theorem is exhibited by giving applications to stability problems.
- S. Bernfeld, G. Ladde, and V. Lakshmikantham, On the classes of differential systems with the desired behavior, Rend. Circ. Mat. Palermo (2) 21 (1972), 85–97. MR 324153, DOI 10.1007/BF02844234
- Fred Brauer, Perturbations of nonlinear systems of differential equations, J. Math. Anal. Appl. 14 (1966), 198–206. MR 192132, DOI 10.1016/0022-247X(66)90021-7 V. Lakshmikantham and S. Leela, Differential and integral inequalities, Theory and Applications, Vols. I, II, Academic Press, New York, 1969.
- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 52 (1975), 181-187
- MSC: Primary 34D20
- DOI: https://doi.org/10.1090/S0002-9939-1975-0372351-6
- MathSciNet review: 0372351