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

Reference:

Logemann, H. and Ryan, E. P., 2010. Volterra functional differential equations: existence, uniqueness, and continuation of solutions. American Mathematical Monthly, 117 (6), pp. 490-511.

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Official URL:

http://dx.doi.org/10.4169/000298910x492790

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.

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