ArticleOriginal scientific text

Title

Some notes on one oscillatory condition of neutral differential equations

Authors 1, 1

Affiliations

  1. Department of Mathematical Analysis, Faculty of Sciences, Šafárik University, Jesenná 5, 041 54 Košice, Slovakia

Abstract

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.

Keywords

neutral equation, oscillatory solution

Bibliography

  1. T.A. Čanturia and R.G. Koplatadze, On oscillatory properties of differential equations with deviating arguments, Tbilisi, Univ. Press, Tbilisi, 1977 (in Russian).
  2. J. Džurina, On unstable neutral differential equations of the second order, Czech. Math. J. 52 (127) (2002), 739-747.
  3. J. Džurina and D. Lacková, Oscillation results for second order nonlinear differential equations, CEJM 2 (1) (2004), 57-66.
  4. L.H. Erbe, Q. Kong and B.G. Zhang, Oscillation theory for functional differential equations, Dekker, New York 1995.
  5. G.B. Gustafson, Bounded oscillation of linear and nonlinear delay differential equations of even order, J. Math. Anal. Appl. 46 (1974), 175-189.
  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.
  7. G.S. Ladde, V. Lakshmikanthan and B.G. Zhang, Oscillation theory of differential equations with deviating arguments, Dekker, New York 1987.
Pages:
103-112
Main language of publication
English
Received
2005-07-08
Published
2006
Exact and natural sciences