Oscillation and Nonoscillation of Difference Equations with Several Delays

KARPUZ B., Stavroulakis I. P.

MEDITERRANEAN JOURNAL OF MATHEMATICS, vol.18, no.1, 2021 (SCI-Expanded, Scopus)

  • Publication Type: Article / Article
  • Volume: 18 Issue: 1
  • Publication Date: 2021
  • Doi Number: 10.1007/s00009-020-01617-0
  • Journal Name: MEDITERRANEAN JOURNAL OF MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, DIALNET
  • Keywords: Oscillation, Nonoscillation, Difference equations, Primary 39A10, Secondary 39A21
  • Dokuz Eylül University Affiliated: Yes

Abstract

Consider the delay difference equation Delta x(n)+Sigma k=1mpk(n)x(n-tau k)=0forn=0,1,...,where Delta is the forward difference operator, i.e., Delta x(n):=x(n+1)-x(n), tau k is a nonnegative integer and {pk(n)}n=0 infinity is a nonnegative sequence of reals for k=1,2,...,m. New oscillation and nonoscillation results, which essentially improve known results in the literature, are established. These results are extended to the more general difference equation Delta x(n)+Sigma k=1mpk(n)x(sigma k(n))=0forn=0,1,....Examples illustrating the significance of the results are given.