COMPARISON THEOREMS ON THE OSCILLATION OF A CLASS OF NEUTRAL DIFFERENCE EQUATIONS WITH CONTINUOUS VARIABLES

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KARPUZ B., Ocalan O.

BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY, vol.47, no.2, pp.401-409, 2010 (SCI-Expanded)

  • Publication Type: Article / Article
  • Volume: 47 Issue: 2
  • Publication Date: 2010
  • Doi Number: 10.4134/bkms.2010.47.2.401
  • Journal Name: BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.401-409
  • Keywords: continuous variable, neutral difference equations, oscillation, positive and negative coefficients, CONTINUOUS ARGUMENTS
  • Open Archive Collection: AVESIS Open Access Collection
  • Akdeniz University Affiliated: No

Abstract

In this paper, we introduce an iterative method to study oscillatory properties of delay difference equations of the following form del(alpha) [x (t) - r (t)x (t - kappa)] + p(t)x(t - tau) - q(t) x (t - sigma) = 0, t >= t(0), where t(0) is an element of R, t varies in the real interval [t(0), infinity), alpha > 0, kappa, tau, sigma >= 0, r is an element of C ([t(0) - alpha, infinity),R(+)), p,q is an element of C ([t(0), infinity), R(+)) and del x (t) = x (t) - x(t - alpha) for t >= t(0).