Oscillation and Nonoscillation of Difference Equations with Several Delays

KARPUZ, BAŞAK; Stavroulakis, Ioannis

doi:10.1007/s00009-020-01617-0

Oscillation and Nonoscillation of Difference Equations with Several Delays

KARPUZ B., Stavroulakis I. P.

MEDITERRANEAN JOURNAL OF MATHEMATICS, cilt.18, sa.1, 2021 (SCI-Expanded, Scopus)

Yayın Türü: Makale / Tam Makale
Cilt numarası: 18 Sayı: 1
Basım Tarihi: 2021
Doi Numarası: 10.1007/s00009-020-01617-0
Dergi Adı: MEDITERRANEAN JOURNAL OF MATHEMATICS
Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, DIALNET
Anahtar Kelimeler: Oscillation, Nonoscillation, Difference equations, Primary 39A10, Secondary 39A21
Dokuz Eylül Üniversitesi Adresli: Evet

Özet

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.