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Oscillations of difference equations with non-monotone retarded arguments

Author

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  • Chatzarakis, G.E.
  • Öcalan, Özkan

Abstract

Consider the first-order retarded difference equationΔx(n)+p(n)xτ(n)=0,n∈N0where (p(n))n⩾0 is a sequence of nonnegative real numbers, and (τ(n))n⩾0 is a sequence of integers such that τ(n)⩽n-1, n⩾0, and limn→∞τ(n)=∞. Under the assumption that the retarded argument is non-monotone, a new oscillation criterion, involving liminf, is established. An example illustrates the case when the result of the paper implies oscillation while previously known results fail.

Suggested Citation

  • Chatzarakis, G.E. & Öcalan, Özkan, 2015. "Oscillations of difference equations with non-monotone retarded arguments," Applied Mathematics and Computation, Elsevier, vol. 258(C), pages 60-66.
    • Handle: RePEc:eee:apmaco:v:258:y:2015:i:c:p:60-66
    DOI: 10.1016/j.amc.2015.01.110
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