Comparison theorems for noncanonical 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 quasiderivatives. We prove comparison theorems on property A between linear and nonlinear equations. Some integral criteria ensuring property A for nonlinear equations are also given. Our assumptions on the nonlinearity of f are restricted to its behavior only in a neighborhood of zero and a neighborhood of infinity.

Słowa kluczowe

EN

Comparison theorem; property A; quasiderivative; noncanonical form; nonlinear equation

Kategorie tematyczne

• 34C10: Oscillation theory, zeros, disconjugacy and comparison theory

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2007
• Tom: 5
• Numer: 1
• Strony: 154-163

Daty

wydano

2007-03-01

online

2007-03-01

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 Analysis, Theory, Methods & Applications, 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”, Proceeding of Dynamic Systems and Applications, Vol. 2, (1996), pp. 99–106.
• [3] M. Cecchi, Z. Došlá and M. Marini: “Asymptotic behavior of solutions of third order delay differential equations”, Archivum Mathematicum(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”, Annali di Matematica pura ed applicata (IV), Vol. CLXXIII, (1997), pp. 373–389. http://dx.doi.org/10.1007/BF01783478
• [6] M. Cecchi, Z. Došlá, M. Marini and Gab. Villari: “On the qualitative behavior of solutions of third order differential equations”, J. Math. Anal. Appl., Vol. 197, (1996), pp. 749–766. http://dx.doi.org/10.1006/jmaa.1996.0050
• [7] J. Džurina: “Property (A) of n-th order ODE’s”, Mathematica Bohemica, Vol. 122(4), (1997), pp. 349–356.
• [8] 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
• [9] I. Mojsej and J. Ohriska: “On solutions of third order nonlinear differential equations”, CEJM, Vol. 4(1), (2006), pp. 46–63.
• [10] J. Ohriska: “Oscillatory and asymptotic properties of third and fourth order linear differential equations”, Czech. Math. J., Vol. 39(114), (1989), pp. 215–224.
• [11] J. Ohriska: “Adjoint differential equations and oscillation”, J. Math. Anal. Appl., Vol. 195, (1995), pp. 778–796. http://dx.doi.org/10.1006/jmaa.1995.1389
• [12] V. Šeda: “Nonoscillatory solutions of differential equations with deviating argument”, Czech. Math. J., Vol. 36(111), (1986), pp. 93–107.

Identyfikatory

DOI

10.2478/s11533-006-0044-3