Sharp oscillation and nonoscillation tests for linear difference equations


KARPUZ B.

JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, vol.23, no.12, pp.1929-1942, 2017 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 23 Issue: 12
  • Publication Date: 2017
  • Doi Number: 10.1080/10236198.2017.1379515
  • Journal Name: JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1929-1942
  • Keywords: Ladas' conjecture, oscillation, nonoscillation, difference equations, PERIODIC-SOLUTIONS, HAMILTONIAN-SYSTEMS, SUBHARMONIC SOLUTIONS, HOMOCLINIC ORBITS, EXISTENCE, STABILITY
  • Dokuz Eylül University Affiliated: Yes

Abstract

We consider difference equations with a single delay term and obtain sufficient conditions for both oscillation and nonoscillation. Moreover, our nonoscillation theorem improves the affirmative answer to Ladas' corrected conjecture given by Tang and Yu in [Comput. Math. Appl. 38(11-12) (1999), pp. 229-237]. We also present a detailed discussion with examples to emphasize the significance and the sharpness of the new results.