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Proceedings of the American Mathematical Society

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Variational comparison theorem and perturbations of nonlinear systems

Author: G. S. Ladde
Journal: Proc. Amer. Math. Soc. 52 (1975), 181-187
MSC: Primary 34D20
MathSciNet review: 0372351
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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.

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  • [1] 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 48 #2505. MR 0324153 (48:2505)
  • [2] F. Brauer, Perturbations of nonlinear systems of differential equations. I, J. Math. Anal. Appl. 14 (1966), 198-206. MR 33 #359. MR 0192132 (33:359)
  • [3] V. Lakshmikantham and S. Leela, Differential and integral inequalities, Theory and Applications, Vols. I, II, Academic Press, New York, 1969.

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Keywords: Differential inequality, generalized variation of constants formula, maximal solution, stability, variational comparison theorem, $ V$-stability, vector Lyapunov-like function
Article copyright: © Copyright 1975 American Mathematical Society

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