The aim of this paper is to present sufficient conditions for all bounded solutions of the second order neutral differential equations of the form (r(t)(x(t) - px(t-τ))')' - q(t)f(x(σ(t))) = 0 to be oscillatory and to compare some existing results.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1067, author = {Bo\v zena Mihal\'\i kov\'a and Eva Chomov\'a}, title = {Some notes on one oscillatory condition of neutral differential equations}, journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization}, volume = {26}, year = {2006}, pages = {103-112}, zbl = {1135.34333}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1067} }
Božena Mihalíková; Eva Chomová. Some notes on one oscillatory condition of neutral differential equations. Discussiones Mathematicae, Differential Inclusions, Control and Optimization, Tome 26 (2006) pp. 103-112. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1067/
[000] [1] T.A. Čanturia and R.G. Koplatadze, On oscillatory properties of differential equations with deviating arguments, Tbilisi, Univ. Press, Tbilisi, 1977 (in Russian).
[001] [2] J. Džurina, On unstable neutral differential equations of the second order, Czech. Math. J. 52 (127) (2002), 739-747. | Zbl 1023.34057
[002] [3] J. Džurina and D. Lacková, Oscillation results for second order nonlinear differential equations, CEJM 2 (1) (2004), 57-66. | Zbl 1046.34058
[003] [4] L.H. Erbe, Q. Kong and B.G. Zhang, Oscillation theory for functional differential equations, Dekker, New York 1995. | Zbl 0821.34067
[004] [5] G.B. Gustafson, Bounded oscillation of linear and nonlinear delay differential equations of even order, J. Math. Anal. Appl. 46 (1974), 175-189. | Zbl 0282.34027
[005] [6] Š. Kulcsár, On the asymptotic behaviour of solutions of the second order neutral differential equations, Publ. Math. Debrecen 57 (1-2) (2000), 153-161. | Zbl 0966.34069
[006] [7] G.S. Ladde, V. Lakshmikanthan and B.G. Zhang, Oscillation theory of differential equations with deviating arguments, Dekker, New York 1987.