Constructive Approach for Solving Nonlinear Singularly Perturbed Systems with Nonconstant Matrix at the Derivative

In this paper we study singularly perturbed systems of differential and integro-differential equations with variable coefficients in the case when a matrix at the derivative is singular. Existence and construction of the solutions are investigated using iterative processes convergent in Cauchy′s sen...

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Bibliographic Details
Published inJournal of mathematical analysis and applications Vol. 196; no. 3; pp. 1008 - 1020
Main Author Slavova, A.
Format Journal Article
LanguageEnglish
Published San Diego, CA Elsevier Inc 15.12.1995
Elsevier
Subjects
Exact sciences and technology
Integral equations
Mathematical analysis
Mathematics
Ordinary differential equations
Sciences and techniques of general use
Singular matrix
Differential equation
Singular perturbation
Iterative process
Periodic solution
Non linear system
Integrodifferential equation
Lyapunov equation
Equation system
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Summary:In this paper we study singularly perturbed systems of differential and integro-differential equations with variable coefficients in the case when a matrix at the derivative is singular. Existence and construction of the solutions are investigated using iterative processes convergent in Cauchy′s sense. For the analysis of these algorithms Lyapunov′s majorizing equations method is applied.
ISSN:0022-247X
1096-0813
DOI:10.1006/jmaa.1995.1457