Electron. J. Differential Equations, Vol. 2016 (2016), No. 311, pp. 1-16.

Systems of advance-delay differential-difference equations and transformation groups

Serguei I. Iakovlev, Valentina Iakovleva

Abstract:
A linear system of mixed-type differential difference equations is studied. A step derivation method and some conditions on an initial function are used to guarantee existence, uniqueness and smoothness of the solution. Further, a transformation group is defined on a complete countably normed space of initial functions and the spectrum of the infinitesimal generator of this group is studied. The same technique applies to a linear system of retarded differential difference equations. A problem to extend solutions of such a system to the left on the real line is solved.

Submitted April 26, 2016. Published December 7, 2016.
Math Subject Classifications: 34K99, 47A10.
Key Words: Advance-delay differential-difference equations; step derivation method; uniqueness; transformation group; infinitesimal generator; point spectrum.

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Serguei I. Iakovlev
Departamento de Matematicas
Universidad Simon Bolivar
Apartado Postal 89000
Caracas 1080-A, Venezuela
email: serguei@usb.ve, serguei.rusa@gmail.com
Valentina Iakovleva
Departamento de Matematicas
Universidad Simon Bolivar
Apartado Postal 89000
Caracas 1080-A, Venezuela
email: romanova@usb.ve, valentina.iakovleva1@gmail.com

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