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Periodic solutions of second-order nonlinear difference equations containing a small parameter

✍ Scribed by Ronald E. Mickens

Publisher
Elsevier Science
Year
1983
Tongue
English
Weight
314 KB
Volume
316
Category
Article
ISSN
0016-0032

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✦ Synopsis

We extend to difference equations the classical method of harmonic balance. We show that the method can be used to obtain an approximation to the periodic solutions of a special class of second-order nonlinear di$erence equations containing a small parameter. Two examples illustrating the method are presented.

πŸ“œ SIMILAR VOLUMES

Periodic solutions of second-order nonli
Periodic solutions of second-order nonlinear difference equations containing a small parameterβ€”II. Equivalent linearization
✍ Ronald E. Mickens πŸ“‚ Article πŸ“… 1985 πŸ› Elsevier Science 🌐 English βš– 325 KB

We extend to a particular class of nonlinear difference equations the classical method of equivalent linearization. We show that the method can be used to obtain an approximation to the periodic solutions of these equations. In particular, we can determine the parameters of the limit cycles and limi

Periodic solutions of second-order nonli
Periodic solutions of second-order nonlinear difference equations containing a small parameterβ€”IV. Multi-discrete time method
✍ Ronald E. Mickens πŸ“‚ Article πŸ“… 1987 πŸ› Elsevier Science 🌐 English βš– 428 KB

We show that a discrete multi-time method can be constructed to obtain approximations to the periodic solutions of a special class of second-order nonlinear difference equations containing a small parameter. Three examples illustrating the method arepresented.

Positive Solutions of Second Order Nonli
Positive Solutions of Second Order Nonlinear Difference Equations
✍ Bing Liu; Sui Sun Cheng πŸ“‚ Article πŸ“… 1996 πŸ› Elsevier Science 🌐 English βš– 131 KB

Necessary and sufficient conditions are obtained for existence of positive solutions of a nonlinear difference equation. Relations between this equation and an advanced type nonlinear difference equation are also discussed.