Forced oscillation of delay difference equations via nonprincipal solution

Ozbekler A.

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, cilt.41, sa.9, ss.3509-3520, 2018 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 41 Sayı: 9
  • Basım Tarihi: 2018
  • Doi Numarası: 10.1002/mma.4843
  • Dergi Adı: MATHEMATICAL METHODS IN THE APPLIED SCIENCES
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.3509-3520
  • Ankara Üniversitesi Adresli: Hayır

Özet

In this paper, we obtain a new oscillation result for delay difference equations of the form Delta(r(n)Delta x(n)) + a(n)x(tau n) = b(n); n is an element of N under the assumption that corresponding homogenous equation Delta(r(n)Delta z(n)) + a(n)z(n+1) = 0; n is an element of N is nonoscillatory, where tau(n) <= n + 1. It is observed that the oscillation behaviormay be altered due to presence of the delay. Extensions to forced Emden-Fowler-type delay difference equations Delta(r(n)Delta x(n)) + a(n)vertical bar x(tau n)vertical bar(alpha-1)x(tau n) = b(n); n is an element of N in the sublinear (0 < alpha < 1) and the superlinear (1 < alpha) cases are also discussed.