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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Variational comparison theorem and perturbations of nonlinear systems


Author: G. S. Ladde
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
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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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DOI: https://doi.org/10.1090/S0002-9939-1975-0372351-6
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