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Mediterranean Journal of Mathematics

, Volume 1, Issue 2, pp 231–240 | Cite as

Oscillation Criteria for First Order Delay Difference Equations

  • Ioannis P. StavroulakisEmail author
Original paper

Abstract

Oscillation criteria for all solutions of the first order delay difference equation of the form

\( x_{n+1}- x_{n} + p_nx_{n-k} = 0, \quad n = 0, 1, 2,..., \)

where {p n } is a sequence of nonnegative real numbers and k is a positive integer are established especially in the case that the well-known oscillation conditions

\(\limsup_{n\rightarrow \infty} \sum^n_{i=n-k} p_i > 1 \quad and \quad \liminf_{n\rightarrow \infty} {1\over k} \sum^{n-1}_{i=n-k} p_i > {k^k\over (k+1)^{k+1}}\)

are not satisfied.

Mathematics Subject Classification (2000).

39A11 

Keywords.

Oscillation Nonoscillation Delay difference equation 

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Copyright information

© Birkhäuser-Verlag 2004

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of IoanninaIoanninaGreece

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