By applying the well-known Leggett-Williams multiple fixed point theorem, this paper investigates the existence of multiple positive periodic solutions of functional differential equations with impulses and a parameter.
Positive periodic solutions of nonlinear functional difference equations depending on a parameter
β Scribed by Yongkun Li; Lifei Zhu; Ping Liu
- Publisher
- Elsevier Science
- Year
- 2004
- Tongue
- English
- Weight
- 321 KB
- Volume
- 48
- Category
- Article
- ISSN
- 0898-1221
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β¦ Synopsis
In
this paper, we use the upper and lower solutions method to show that there exists a A*, such that the nonlinear functional difference equation of the form
has at least one positive T-periodic solutions for A E (0, A*] and does not have any positive T-periodic solutions for A > A*, where a(n), h(n), and ~-(n) are T-periodic functions. @
π SIMILAR VOLUMES
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
Consider the following non-autonomous first order functional difference equation It is shown that, under certain assumptions, there exist positive periodic solutions. Applications are given to illustrate the main results.