On solutions of third order nonlinear differential equations

• Autorzy: Ivan Mojsej , Ján Ohriska
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Oscillation theory; nonlinear equation; deviating argument; quasiderivatives; 34K11

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2006
• Tom: 4
• Numer: 1
• Strony: 46-63

Daty

wydano

2006-03-01

online

2006-03-01

Twórcy

autor

Ivan Mojsej

• P. J. Šafárik University

autor

Ján Ohriska

• P. J. Šafárik University

Bibliografia

• [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
• [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.
• [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.
• [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
• [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
• [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

Identyfikatory

DOI

10.1007/s11533-005-0004-3