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.
 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-X10.1016/S0362-546X(97)00028-XSearch in Google Scholar
 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. Search in Google Scholar
 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. Search in Google Scholar
 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:102287880406510.1023/A:1022878804065Search in Google Scholar
 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/BF0178347810.1007/BF01783478Search in Google Scholar
 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.1996.005010.1006/jmaa.1996.0050Search in Google Scholar
 J. Džurina: “Property (A) of n-th order ODE’s”, Mathematica Bohemica, Vol. 122(4), (1997), pp. 349–356. Search in Google Scholar
 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/0333050910.2969/jmsj/03330509Search in Google Scholar
 I. Mojsej and J. Ohriska: “On solutions of third order nonlinear differential equations”, CEJM, Vol. 4(1), (2006), pp. 46–63. Search in Google Scholar
 J. Ohriska: “Oscillatory and asymptotic properties of third and fourth order linear differential equations”, Czech. Math. J., Vol. 39(114), (1989), pp. 215–224. Search in Google Scholar
 J. Ohriska: “Adjoint differential equations and oscillation”, J. Math. Anal. Appl., Vol. 195, (1995), pp. 778–796. http://dx.doi.org/10.1006/jmaa.1995.138910.1006/jmaa.1995.1389Search in Google Scholar
 V. Šeda: “Nonoscillatory solutions of differential equations with deviating argument”, Czech. Math. J., Vol. 36(111), (1986), pp. 93–107. Search in Google Scholar
© 2007 Versita Warsaw
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.