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Some Results on Stability of Retarded Functional Differential Equations Using Dichotomic Map Techniques

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Abstract

This paper deals with the study of the stability of nonautonomous retarded functional differential equations using the theory of dichotomic maps. After some preliminaries, we prove the theorems on simple and asymptotic stability. Some examples are given to illustrate the application of the method. Main results about asymptotic stability of the equation \(x'(t) = - b(t)x(t - r)\) and of itsnonlinear generalization\(x'(t) = b(t)f(x(t - r))\) are established.

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Authors and Affiliations

  1. Departamento de Física e Matemática, Faculdade de Filosofia, Ciências e Letras de Ribeirão Preto – USP, 14040-901-Ribeirão Preto, SP, Brazil

    Maria Aparecida Bená

  2. Departamento de Matemática, Faculdade de Ciências – UNESP, 17033-360-Bauru, SP, Brazil

    José Geraldo Dos Reis

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  1. Maria Aparecida Bená
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  2. José Geraldo Dos Reis
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Aparecida Bená, M., Dos Reis, J.G. Some Results on Stability of Retarded Functional Differential Equations Using Dichotomic Map Techniques. Positivity 2, 229–238 (1998). https://doi.org/10.1023/A:1009742807025

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  • DOI: https://doi.org/10.1023/A:1009742807025

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