Some observations on a Conti's result

Adrian Constantin

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1991)

  • Volume: 2, Issue: 2, page 137-145
  • ISSN: 1120-6330

Abstract

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An extension of a result of R. Conti is given from which some integro-differential inequalities of the Gronwall-Bellman-Bihari type and a criterion for the continuation of solutions of a system of ordinary differential equations are deduced.

How to cite

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Constantin, Adrian. "Some observations on a Conti's result." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 2.2 (1991): 137-145. <http://eudml.org/doc/244140>.

@article{Constantin1991,
abstract = {An extension of a result of R. Conti is given from which some integro-differential inequalities of the Gronwall-Bellman-Bihari type and a criterion for the continuation of solutions of a system of ordinary differential equations are deduced.},
author = {Constantin, Adrian},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Ordinary differential equations; Comparison method; Inequalities; system of ordinary differential equations; integral inequalities; Wong; Viswanatham; Gronwall-Bellman; Bihari; Pachpatte},
language = {eng},
month = {6},
number = {2},
pages = {137-145},
publisher = {Accademia Nazionale dei Lincei},
title = {Some observations on a Conti's result},
url = {http://eudml.org/doc/244140},
volume = {2},
year = {1991},
}

TY - JOUR
AU - Constantin, Adrian
TI - Some observations on a Conti's result
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1991/6//
PB - Accademia Nazionale dei Lincei
VL - 2
IS - 2
SP - 137
EP - 145
AB - An extension of a result of R. Conti is given from which some integro-differential inequalities of the Gronwall-Bellman-Bihari type and a criterion for the continuation of solutions of a system of ordinary differential equations are deduced.
LA - eng
KW - Ordinary differential equations; Comparison method; Inequalities; system of ordinary differential equations; integral inequalities; Wong; Viswanatham; Gronwall-Bellman; Bihari; Pachpatte
UR - http://eudml.org/doc/244140
ER -

References

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  1. BELLMAN, R., The stability of solutions of linear differential equations. Duke Math. J., 10, 1943, 643-647. Zbl0061.18502MR9408
  2. BIHARI, I., A generalization of a lemma of Bellman and its application to uniqueness problems of differential equations. Acta Math. Sci. Hungar., 7, 1956, 71-94. Zbl0070.08201MR79154
  3. CONTI, R., Limitazioni «in ampiezza» delle soluzioni di un sistema di equazioni differenziali e applicazioni. Boll. U.M.I., 11, 1956, 344-350. Zbl0071.30601MR80829
  4. CONTI, R., Sulla prolungabilità delle soluzioni di un sistema di equazioni differenziali ordinarie. Boll. U.M.I., 11, 1956, 510-514. Zbl0072.30403MR83628
  5. CONTI, R. - SANSONE, G., Equazioni differenziali non lineari. Monografie Matematiche del C.N.R., 3, Roma1956. Zbl0075.26803MR88607
  6. KATO, J. - STRAUSS, A., On the global existence of solutions and Liapunov functions. Annali Mat. Pura Appl., 1967. Zbl0155.13802MR226130
  7. LAKSHMIKANTHAM, V., A variation of constants formula and Bellman-Gronwall-Reid inequalities. J. Math. Anal. Appl., 41, 1973, 199-204. Zbl0251.34009MR320414
  8. MORRO, A., A Gronwall-like inequality and its applications to continuum thermodynamics. Boll. U.M.I., 6, 1982, 553-562. Zbl0498.34036MR666586
  9. LA SALLE, J. P. - LEFSCHETZ, S., Stability by Liapunov's Direct Method with Applications. Academic Press, New York1961. Zbl0098.06102
  10. PACHPATTE, B. G., A note on Gronwall-Bellman inequality. J. Math. Anal. Appl., 44, 1973, 758-762. Zbl0274.45011MR335721
  11. STRAUSS, A., A note on a global existence result of R. Conti.Boll. U.M.I., 22, 1967, 434-441. Zbl0155.13801MR226083
  12. VISWANATHAN, B., A generalization of Bellman' lemma. Proc. Amer. Math. Soc, 14, 1963, 15-18. Zbl0118.08001
  13. WONG, J. S. W., On an integral inequality of Gronwall. Revue Roum. Math. Pures Appl., 10, 1967, 1519-1522. Zbl0156.30902MR226116
  14. YOSHIZAWA, T., Stability Theory by Liapunov's Second Method. Math. Soc. Japan, Tokyo1966. Zbl0144.10802MR208086
  15. DIEUDONNÉ, J., Foundations of Modern Analysis. Academic Press, New York1960, 154. Zbl0176.00502MR120319
  16. BOURBAKI, N., Éléments de mathématique. Livre IV, Fonctions d'une variable réelle. Hermann & C.ie Editeurs, Paris1951, 22. MR45774

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