Necessary Conditions for the Solutions of Second Order Non-linear Neutral Delay Difference Equations to Be Oscillatory or Tend to Zero

Autor: R. N. Rath, J. G. Dix, B. L. S. Barik, B. Dihudi
Jazyk: angličtina
Rok vydání: 2007
Předmět:
Zdroj: International Journal of Mathematics and Mathematical Sciences, Vol 2007 (2007)
Druh dokumentu: article
ISSN: 0161-1712
1687-0425
DOI: 10.1155/2007/60907
Popis: We find necessary conditions for every solution of the neutral delay difference equation Δ(rnΔ(yn−pnyn−m))+qnG(yn−k)=fn to oscillate or to tend to zero as n→∞, where Δ is the forward difference operator Δxn=xn+1−xn, and pn, qn, rn are sequences of real numbers with qn≥0, rn>0. Different ranges of {pn}, including pn=±1, are considered in this paper. We do not assume that G is Lipschitzian nor nondecreasing with xG(x)>0 for x≠0. In this way, the results of this paper improve, generalize, and extend recent results. Also, we provide illustrative examples for our results.
Databáze: Directory of Open Access Journals
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