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Existence of solutions of multi-valued Urysohn integral equations

  • T. S. Angell
Contributed Papers

Abstract

We prove the existence of a solution of an integral inclusion of Urysohn type with delay. By imposing standard boundedness, convexity, and semicontinuity conditions on the set-valued mapping defining the integral inclusion, we show that the right-hand side of the relation constitutes a mapping defined on a suitable Banach space and satisfying the conditions of Kakutani's theorem for the existence of a fixed point of a set-valued mapping. By introducing the notion of generalized or chattering state solutions, we show how the convexity requirements may be relaxed.

Key Words

Urysohn equations delay systems set-valued mappings Kakutani's theorem semicontinuity 

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Copyright information

© Plenum Publishing Corporation 1985

Authors and Affiliations

  • T. S. Angell
    • 1
  1. 1.Department of Mathematical SciencesUniversity of DelawareNewark

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