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Asymptotic Formulas for the Solutions of Integro-Differential Equations

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Abstract

We study the problem of asymptotic integration of the linear integro-differential equation

$$x^{(n)} (t) + a_{n - 1} (t)x^{(n - 1)} (t) + ... + a_0 (t)x(t) = \int_0^t {K(t,s)x(s)ds} $$

, and the achievement of an asymptotic formula for the solutions of the equation

$$x^{(n)} (t) + a_{n - 1} (t)x^{(n - 1)} (t) + ... + a_0 (t)x(t) = \int_0^t {K(t,s)x(s)ds} + f(t)$$

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Authors and Affiliations

  1. Departamento de Matemáticas, Universidad De Orjente, Cumaná, 6101-A, Apartado 245, Venezuela E-mail

    R. Naulin

  2. Departamento de Matemáticas, Universidad Simón Bolívar, Caracas, Apartado, 89000, Venezuela E-mail

    C.J. Vanegas

Authors
  1. R. Naulin
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  2. C.J. Vanegas
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Naulin, R., Vanegas, C. Asymptotic Formulas for the Solutions of Integro-Differential Equations. Acta Mathematica Hungarica 89, 281–299 (2000). https://doi.org/10.1023/A:1006702219824

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