Existence and asymptotic behavior of solutions of nonlinear neutral differential equations

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1 Citation (Scopus)

Abstract

The nonlinear neutral differential equation dn/dt n[x(t)+h(t)x(τ(t))]+f(t,x(g(t)))=q(t), is considered under the following conditions: n∈N; h∈C[t0,∞); τ∈C[t0,∞) is strictly increasing, limt→∞τ(t)=∞ and τ(t)<t for t>t0; g∈C[t0,∞) and lim t→∞g(t)=∞; f∈C([t0,∞)×R) ; q∈C[t0,∞). It is shown that if f is small enough in some sense, Eq. (1) has a solution x(t) which behaves like the solution of the unperturbed equation dn/dtn[ω(t)+h(t) ω(τ(t))]=q(t). Several known results in the literature can be obtained from our results.

Original languageEnglish
Pages (from-to)536-562
Number of pages27
JournalMathematical and Computer Modelling
Volume43
Issue number5-6
DOIs
Publication statusPublished - 2006 Mar
Externally publishedYes

Keywords

  • Neutral differential equation
  • Nonoscillatory solution
  • Oscillatory solution

ASJC Scopus subject areas

  • Modelling and Simulation
  • Computer Science Applications

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