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Czechoslovak Mathematical Journal

, Volume 55, Issue 1, pp 237–253 | Cite as

Existence for nonoscillatory solutions of higher order nonlinear neutral differential equations

  • Yong Zhou
  • B. G. Zhang
  • Y. Q. Huang
Article

Abstract

Consider the forced higher-order nonlinear neutral functional differential equation
$$\frac{{d^n }}{{dt^n }}\left[ {x\left( t \right) + C\left( t \right)x\left( {t - \tau } \right)} \right] + \sum\limits_{i = 1}^m {Q_i } \left( t \right)f_i \left( {x\left( {t - \sigma _i } \right)} \right) = g\left( t \right),\quad t \geqslant t_0 ,$$
where n,m ≥, 1 are integers, τ, σi ∈ ℝ+ = [0,∞), C,Q i, gC([t 0,∞), ℝ), fiC(ℝ, ℝ), (i = 1, 2, ...;, m). Some sufficient conditions for the existence of a nonoscillatory solution of above equation are obtained for general Q i(t) (i = 1, 2, ... ,m) and g(t) which means that we allow oscillatory Q i(t) (i = 1, 2, ... ,m) and g(t). Our results improve essentially some known results in the references.

Keywords

neutral differential equations nonoscillatory solutions 

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Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • Yong Zhou
    • 1
  • B. G. Zhang
    • 2
  • Y. Q. Huang
    • 3
  1. 1.Department of MathematicsXiangtan UniversityHunanP.R. China
  2. 2.Department of Applied MathematicsOcean University of QingdaoQingdaoP.R. China
  3. 3.Department of MathematicsXiangtan UniversityXiangtanP.R. China

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