Volterra functional differential equations: existence, uniqueness, and continuation of solutions

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Abstract

The initial-value problem for a class of Volterra functional differential equations- of sufficient generality to encompass, as special cases, ordinary differential equations, retarded differential equations, integro-differential equations, and hysteretic differential equations- is studied. A self-contained and elementary treatment of this over-arching problem is provided, in which a unifying theory of existence, uniqueness, and continuation of solutions is developed. As an illustrative example, a controlled differential equation with hysteresis is considered.
Original languageEnglish
Pages (from-to)490-511
Number of pages22
JournalAmerican Mathematical Monthly
Volume117
Issue number6
DOIs
Publication statusPublished - Jun 2010

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