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A Nonlinear Variation of Constants Method for Integro-Differential and Integral Equations

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A Nonlinear Variation of Constants Method for Integro-Differential and Integral Equations

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Title: A Nonlinear Variation of Constants Method for Integro-Differential and Integral Equations
Author: Lord, M. E.; Bernfeld, Stephen R.
Abstract: It is well known that a very important technique in obtaining the asymptotic behavior of solutions of linear and nonlinear ordinary differential equations under perturbations is through the use of the variation of constants formula (see [1] and [14]). Miller [16] used a well known representation formula for perturbed linear Volterra integral equations in terms of the resolvent which has been successfully used in recent years to analyze stability behavior of solutions (see, for example, [12] and [17] and references therein). In addition, Bownds and Cushing [4] obtained another variation of constants formula for linear integral equations utilizing a fundamental matrix, and thus extended in a very natural manner the formula used in ordinary differential equations. Using this formula in [5] and [6] they have obtained significant results in the stability of perturbed linear integral equations and have successfully demonstrated the contrasts and similarities between stability theory of integral equations and that of ordinary differential equations.
URI: http://hdl.handle.net/10106/2194
Date: 1976-02

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