On solutions of third order nonlinear differential equations

Ivan Mojsej; Ján Ohriska

Open Mathematics (2006)

  • Volume: 4, Issue: 1, page 46-63
  • ISSN: 2391-5455

Abstract

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The aim of our paper is to study oscillatory and asymptotic properties of solutions of nonlinear differential equations of the third order with deviating argument. In particular, we prove a comparison theorem for properties A and B as well as a comparison result on property A between nonlinear equations with and without deviating arguments. Our assumptions on nonlinearity f are related to its behavior only in a neighbourhood of zero and/or of infinity.

How to cite

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Ivan Mojsej, and Ján Ohriska. "On solutions of third order nonlinear differential equations." Open Mathematics 4.1 (2006): 46-63. <http://eudml.org/doc/268806>.

@article{IvanMojsej2006,
abstract = {The aim of our paper is to study oscillatory and asymptotic properties of solutions of nonlinear differential equations of the third order with deviating argument. In particular, we prove a comparison theorem for properties A and B as well as a comparison result on property A between nonlinear equations with and without deviating arguments. Our assumptions on nonlinearity f are related to its behavior only in a neighbourhood of zero and/or of infinity.},
author = {Ivan Mojsej, Ján Ohriska},
journal = {Open Mathematics},
keywords = {34K11},
language = {eng},
number = {1},
pages = {46-63},
title = {On solutions of third order nonlinear differential equations},
url = {http://eudml.org/doc/268806},
volume = {4},
year = {2006},
}

TY - JOUR
AU - Ivan Mojsej
AU - Ján Ohriska
TI - On solutions of third order nonlinear differential equations
JO - Open Mathematics
PY - 2006
VL - 4
IS - 1
SP - 46
EP - 63
AB - The aim of our paper is to study oscillatory and asymptotic properties of solutions of nonlinear differential equations of the third order with deviating argument. In particular, we prove a comparison theorem for properties A and B as well as a comparison result on property A between nonlinear equations with and without deviating arguments. Our assumptions on nonlinearity f are related to its behavior only in a neighbourhood of zero and/or of infinity.
LA - eng
KW - 34K11
UR - http://eudml.org/doc/268806
ER -

References

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  1. [1] M. Cecchi, Z. Došlá and M. Marini: “On nonlinear oscillations for equations associated to disconjugate operators”, Nonlinear Anal.-Theor., Vol. 30(3), (1997), pp. 1583–1594. http://dx.doi.org/10.1016/S0362-546X(97)00028-X Zbl0892.34032
  2. [2] M. Cecchi, Z. Došlá and M. Marini: “Comparison theorems for third order differential equations”, Proc. Dynam. Systems Appl., Vol. 2, (1996), pp. 99–106. Zbl0873.34021
  3. [3] M. Cecchi, Z. Došlá and M. Marini: “Asymptotic behavior of solutions of third order delay differential equations”, Arch. Math. (Brno), Vol. 33, (1997), pp. 99–108. Zbl0916.34059
  4. [4] M. Cecchi, Z. Došlá and M. Marini: “Some properties of third order differential operators”, Czech. Math. J., Vol. 47(122), (1997), pp. 729–748. http://dx.doi.org/10.1023/A:1022878804065 Zbl0903.34032
  5. [5] M. Cecchi, Z. Došlá and M. Marini: “An Equivalence Theorem on Properties A, B for Third Order Differential Equations”, Ann. Mat. Pura Appl. (IV), Vol. CLXXIII, (1997), pp. 373–389. http://dx.doi.org/10.1007/BF01783478 Zbl0937.34029
  6. [6] T. Kusano and M. Naito: “Comparison theorems for functional differential equations with deviating arguments”, J. Math. Soc. Japan, Vol. 33(3), (1981), pp. 509–532. http://dx.doi.org/10.2969/jmsj/03330509 Zbl0494.34049

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