| Abstrakt: |
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 2 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. [ABSTRACT FROM AUTHOR] |
