Some Oscillation and Non-Oscillation Theorems for Fourth Order Difference Equations | Zendy

E. Thandapani | Zendy; I. M. Arockiasamy | Zendy

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Some Oscillation and Non-Oscillation Theorems for Fourth Order Difference Equations

Author(s) -

E. Thandapani,

I. M. Arockiasamy

Publication year - 2000

Publication title -

zeitschrift für analysis und ihre anwendungen

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.567

H-Index - 35

eISSN - 1661-4534

pISSN - 0232-2064

DOI - 10.4171/zaa/985

Subject(s) - oscillation (cell signaling) , order (exchange) , mathematics , mathematical analysis , physics , chemistry , economics , biochemistry , finance

Sufficient conditions are established for oscillation of all solutions of the fourth order difference equation ∆ an∆(bn∆(cn∆yn)) + qnf(yn+1) = hn (n ∈ N0) where ∆ is the forward difference operator ∆yn = yn+1 − yn, {an}, {bn}, {cn}, {qn}, {hn} are real sequences, and f is a real-valued continuous function. Also, sufficient conditions are provided which ensure that all non-oscillatory solutions of the equation approach zero as n →∞. Examples are inserted to illustrate the results.

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