Relations among various criteria of uniqueness for ordinary differential equations

Józef Banaś; Andrzej Hajnosz; Stanisław Wędrychowicz

Commentationes Mathematicae Universitatis Carolinae (1981)

  • Volume: 022, Issue: 1, page 59-70
  • ISSN: 0010-2628

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Banaś, Józef, Hajnosz, Andrzej, and Wędrychowicz, Stanisław. "Relations among various criteria of uniqueness for ordinary differential equations." Commentationes Mathematicae Universitatis Carolinae 022.1 (1981): 59-70. <http://eudml.org/doc/17087>.

@article{Banaś1981,
author = {Banaś, Józef, Hajnosz, Andrzej, Wędrychowicz, Stanisław},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {uniqueness criterion; Kamke comparison function},
language = {eng},
number = {1},
pages = {59-70},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Relations among various criteria of uniqueness for ordinary differential equations},
url = {http://eudml.org/doc/17087},
volume = {022},
year = {1981},
}

TY - JOUR
AU - Banaś, Józef
AU - Hajnosz, Andrzej
AU - Wędrychowicz, Stanisław
TI - Relations among various criteria of uniqueness for ordinary differential equations
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1981
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 022
IS - 1
SP - 59
EP - 70
LA - eng
KW - uniqueness criterion; Kamke comparison function
UR - http://eudml.org/doc/17087
ER -

References

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  1. J. BANAŚ A. HAJNOSZ S. WEDRYCHOWICZ, Some generalization of Szufla's theorem for ordinary differential equationa in Banach spaces, Bull. Acad. Polon. Sci. (preprint). 
  2. E. BOMPIANI, Un teorema di confronto ed un teorema di unicita per l’equazione differenziale y ' = f ( x , y ) , Atti Accad. Naz. Lincei. Rend. Classe Sci. Fis. Mat. Nat. 6,1 (1925), 298-302. (1925) 
  3. F. CAFIERO, Su due teoremi di confronto relativi ad un'quazione differenziale del ordinaria del primo ordine, Boll. Univ. Mat. Ital. 3, 3 (1948), 124-128. (1948) MR0027392
  4. E. A. CODDINGTON N. LEVINSON, Theory of ordinary differential equations, New Tork - Toronto - London, McGraw-Hill Book Co., 1955. (1955) MR0069338
  5. K. DEIMLING, Ordinary differential equations in Banach spaces, Lecture Notes in Mathematics, 596, Springer Verlag, 1977. (1977) Zbl0361.34050MR0463601
  6. K. GOEBEL W. RZYMOWSKI, An existence theorem for the equations x ' = f ( t , x ) in Banach space, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 18, 7 (1970), 367-370. (1970) MR0269957
  7. P. HARTMAN, Ordinary differential equations, New York - London - Sydney, John Wiley, 1964. (1964) Zbl0125.32102MR0171038
  8. E. KAMKE, Über die eindeutige Bestimmtheit der Integrale von Differentialgleichungen, Math. Z. 32 (1930), 101-107. (1930) MR1545153
  9. J. KISYŃSKI, Sur les équations différentielles dans les espaces de Banach, Bull. Acad. Polon. Sei. Sér. Sci. Math. Astronom. Phys. 7 (1959), 381-385. (1959) MR0111919
  10. C. OLECH, Remarks concerning criteria for uniqueness of solutions of ordinary differential equations, ibidem, 8 (1960), 661-666. (1960) Zbl0173.33701MR0132228
  11. C. OLECH A. PLIŚ, Monotonocity assumptions in uniqueness criteria for differential equations, Colloq. Math. 18 (1967), 43-58. (1967) MR0224886
  12. O. PERRON, Über Ein- und Mehrdeutigkeit des Integrals eines Systems von Differentialgleichungen, Math. Ann. 95 (1926), 98-101. (1926) MR1512265
  13. J. SZARSKI, Differential inequalities, Monografie Matematyczne 43, Warszawa 1965. (1965) Zbl0135.25804MR0190409
  14. W. WALTER, Bemerkungen zu verschiedenen Eindeutigkeitskriterien für gewöhnliche Differentialgleichungen, Math. Z. 84 (1964), 222-227. (1964) Zbl0125.04401MR0167676
  15. W. WALTER, Differential and integral inequalities, Ergebnisse der Mathematik und ihrer Grenzgebiete, 55, Springer Verlag, 1970. (1970) Zbl0252.35005MR0271508

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