Nonoscillation and oscillation of solutions of a class of third order difference equations

• Published in: Journal of mathematical analysis and applications Vol. 336; no. 1; pp. 213 - 223
• Main Authors: Parhi, N., Panda, Anita
• Format: Journal Article
• Language: English
• Published: San Diego, CA Elsevier Inc 01.12.2007; Elsevier
• Subjects: Difference and functional equations, recurrence relations; Exact sciences and technology; Finite differences and functional equations; Mathematical analysis; Mathematics; Nonoscillation; Numerical analysis; Numerical analysis. Scientific computation; Oscillation; Sciences and techniques of general use; Third order nonlinear difference equations; Nonoscillation; Third order nonlinear difference equations; Oscillation; Non linear equation; Sufficient condition; Third order equation; Mathematical analysis; Difference equation; Application
• ISSN: 0022-247X; 1096-0813
• DOI: 10.1016/j.jmaa.2007.02.054

In this paper, sufficient conditions are obtained for nonoscillation/oscillation of all solutions of a class of nonlinear third order difference equations of the form Δ a ( p n Δ a 2 y n ) + q n Δ a 2 y n = f ( n , y n , Δ a y n , Δ a 2 y n ) involving the generalized difference operator Δ a which is defined as Δ a y n = y n + 1 − a y n , a ≠ 0 .