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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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dc.contributor.author Lord, M. E. en
dc.contributor.author Bernfeld, Stephen R. en
dc.date.accessioned 2010-06-01T18:27:59Z en
dc.date.available 2010-06-01T18:27:59Z en
dc.date.issued 1976-02 en
dc.identifier.uri http://hdl.handle.net/10106/2194 en
dc.description.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. en
dc.language.iso en_US en
dc.publisher University of Texas at Arlington en
dc.relation.ispartofseries Technical Report;38 en
dc.subject Integral Equations en
dc.subject Variation of parameters en
dc.subject Integro-differential equation en
dc.subject Variation of constants en
dc.subject Perturbed linear en
dc.subject.lcsh Mathematics Research en
dc.title A Nonlinear Variation of Constants Method for Integro-Differential and Integral Equations en
dc.type Technical Report en
dc.publisher.department Department of Mathematics en

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