Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)

  • [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.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 34D20

Retrieve articles in all journals with MSC: 34D20


Additional Information

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

American Mathematical Society