Nonuniqueness results for ordinary differential equations

Josef Kalas

Czechoslovak Mathematical Journal (1998)

  • Volume: 48, Issue: 2, page 373-384
  • ISSN: 0011-4642

Abstract

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In the present paper we give general nonuniqueness results which cover most of the known nonuniqueness criteria. In particular, we obtain a generalization of the nonuniqueness theorem of Chr. Nowak, of Samimi’s nonuniqueness theorem and of Stettner’s nonuniqueness criterion.

How to cite

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Kalas, Josef. "Nonuniqueness results for ordinary differential equations." Czechoslovak Mathematical Journal 48.2 (1998): 373-384. <http://eudml.org/doc/30426>.

@article{Kalas1998,
abstract = {In the present paper we give general nonuniqueness results which cover most of the known nonuniqueness criteria. In particular, we obtain a generalization of the nonuniqueness theorem of Chr. Nowak, of Samimi’s nonuniqueness theorem and of Stettner’s nonuniqueness criterion.},
author = {Kalas, Josef},
journal = {Czechoslovak Mathematical Journal},
keywords = {uniqueness and nonuniqueness of solutions; singular Cauchy problem; Lyapunov functions},
language = {eng},
number = {2},
pages = {373-384},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Nonuniqueness results for ordinary differential equations},
url = {http://eudml.org/doc/30426},
volume = {48},
year = {1998},
}

TY - JOUR
AU - Kalas, Josef
TI - Nonuniqueness results for ordinary differential equations
JO - Czechoslovak Mathematical Journal
PY - 1998
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 48
IS - 2
SP - 373
EP - 384
AB - In the present paper we give general nonuniqueness results which cover most of the known nonuniqueness criteria. In particular, we obtain a generalization of the nonuniqueness theorem of Chr. Nowak, of Samimi’s nonuniqueness theorem and of Stettner’s nonuniqueness criterion.
LA - eng
KW - uniqueness and nonuniqueness of solutions; singular Cauchy problem; Lyapunov functions
UR - http://eudml.org/doc/30426
ER -

References

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  1. Uniqueness and Nonuniqueness Criteria for Ordinary Differential Equations, World Scientific, 1993. (1993) MR1336820
  2. Nonuniqueness for the solutions of ordinary differential equations, Czechoslovak Math. Journal 29 (1979), 105–112. (1979) Zbl0396.34006MR0518144
  3. On the Kamke’s function in the uniqueness theorem of ordinary differential equations, Proc. Nat. Acad. Sci. India Ser. A 34 (1964), 11–14. (1964) Zbl0166.34103MR0218635
  4. Differential and Integral Inequalities, Vol. I, Academic Press, New York, 1969. (1969) 
  5. 10.1080/00036819208840130, Applicable Anal. 47 (1992), 39–44. (1992) Zbl0792.34002MR1214647DOI10.1080/00036819208840130
  6. Uniqueness and nonuniqueness results for ordinary differential equations, (manuscript). Zbl0882.34003
  7. 10.1080/00036818208839400, Applicable Anal. 13 (1982), 291–296. (1982) Zbl0464.34005MR0670663DOI10.1080/00036818208839400
  8. 10.1002/mana.19740640113, Math. Nachrichten 64 (1974), 233–237. (1974) Zbl0297.34003MR0357933DOI10.1002/mana.19740640113

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