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Fourt-order nonlinear oscillations of difference equations

✍ Scribed by E. Thandapani; I.M. Arockiasamy

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 473 KB
Volume: 42
Category: Article
ISSN: 0898-1221
DOI: 10.1016/s0898-1221(01)00160-2

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✦ Synopsis

The authors consider the fourth-order difference equation ~2(r,~2yn)÷f(n, yn)=O, n E N(n0), (,) where f(n, u) may be classified as superlinear, sublinear, strongly superlinear, and strongly sublinear and Y~=no(n/rn) < oc. In superlinear and sublinear cases, necessm'y and sufficient conditions are obtained for the existence of nonoscillatory solutions of (*) with a specified asymptotic behavior. Further, in strongly superlinear and strongly sublinear cases, necessary and sufficient conditions are given for all solutions of (*) to be oscillatory.

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