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Ukrainian Mathematical Journal

, Volume 55, Issue 12, pp 2006–2030 | Cite as

Infinite Systems of Hyperbolic Functional Differential Equations

  • Z. Kamont
Article

Abstract

We consider initial-value problems for infinite systems of first-order partial functional differential equations. The unknown function is the functional argument in equations and the partial derivations appear in the classical sense. A theorem on the existence of a solution and its continuous dependence upon initial data is proved. The Cauchy problem is transformed into a system of functional integral equations. The existence of a solution of this system is proved by using integral inequalities and the iterative method. Infinite differential systems with deviated argument and differential integral systems can be derived from the general model by specializing given operators.

Keywords

Integral Equation Initial Data General Model Cauchy Problem Unknown Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Plenum Publishing Corporation 2003

Authors and Affiliations

  • Z. Kamont
    • 1
  1. 1.Gdańsk University of TechnologyGdańskPoland

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