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Linear approximation and asymptotic expansion associated with the system of nonlinear functional equations

Ngoc L. T. P., Dung H. T. H., Danh P. H., Long N. T.

Demonstratio Mathematica

2014

Vol. 47, nr 1

103--124

This paper is devoted to the study of the following perturbed system of nonlinear functional equations (…) , where ε is a small parameter, aijk; bijk are the given real constants, Rijk; Sijk; Xijk : (…) are the given continuous functions and (…) 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 (…) ; we investigate the quadratic convergence of (E). Finally, in the case of (…) 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.

On a nonlinear Kirchhoff-Carrier wave equation in the unit membrane: the quadratic convergence and asymptotic expansion of solutions

Long N., Ngoc L.

Demonstratio Mathematica

2007

Vol. 40, nr 2

365-392

In this paper we consider the initial-boundary value problem for the nonlinear wave equation.

Extended method of quasilinearization for a nonlinear three-point boundary value problem

Ahmad B., Alsaedi A., Garout D.

Demonstratio Mathematica

2006

Vol. 39, nr 4

803-814

In this paper, we discuss the generalized quasilinearization technique for a second order nonlinear differential equation with nonlinear three-point general boundary conditions. In fact, we obtain sequences of upper and lower solutions converging mono- tonically and quadratically to the unique solution of the nonlinear three-point boundary value problem.