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.
@article{bwmeta1.element.doi-10_1007_s11533-005-0004-3,
author = {Ivan Mojsej and J\'an Ohriska},
title = {On solutions of third order nonlinear differential equations},
journal = {Open Mathematics},
volume = {4},
year = {2006},
pages = {46-63},
zbl = {1104.34048},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1007_s11533-005-0004-3}
}
Ivan Mojsej; Ján Ohriska. On solutions of third order nonlinear differential equations. Open Mathematics, Tome 4 (2006) pp. 46-63. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1007_s11533-005-0004-3/
[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 | Zbl 0892.34032
[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. | Zbl 0873.34021
[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. | Zbl 0916.34059
[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 | Zbl 0903.34032
[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 | Zbl 0937.34029
[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 | Zbl 0494.34049