Linear Approximation And Asymptotic Expansion Associated With The System Of Nonlinear Functional Equations
| Autor: | Ngoc Le Thi Phuong, Dung Huynh Thi Hoang, Danh Pham Hong, Long Nguyen Thanh |
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| Jazyk: | angličtina |
| Rok vydání: | 2014 |
| Předmět: | |
| Zdroj: | Demonstratio Mathematica, Vol 47, Iss 1, Pp 103-124 (2014) |
| Druh dokumentu: | article |
| ISSN: | 0420-1213 2391-4661 |
| DOI: | 10.2478/dema-2014-0008 |
| Popis: | This paper is devoted to the study of the following perturbed system of nonlinear functional equations x ∊Ω=[-b,b], i = 1,…., n; where ε is a small parameter, aijk; bijk are the given real constants, Rijk, Sijk , Xijk : Ω → Ω ,gi → Ω →ℝ , Ψ: Ω x ℝ2→ ℝ are the given continuous functions and ƒi :Ω →ℝ are unknown functions. First, by using the Banach fixed point theorem, we find sufficient conditions for the unique existence and stability of a solution of (E). Next, in the case of Ψ ∊ C2(Ω x ℝ2; ℝ); we investigate the quadratic convergence of (E). Finally, in the case of Ψ ∊ CN(Ω x ℝ2; ℝ) and ε sufficiently small, we establish an asymptotic expansion of the solution of (E) up to order N + 1 in ε. In order to illustrate the results obtained, some examples are also given |
| Databáze: | Directory of Open Access Journals |
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