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    STUDIA MATHEMATICA - Issue no. 1 / 2020  
         
  Article:   INTEGRODIFFERENTIAL EVOLUTION SYSTEMS WITH NONLOCAL INITIAL CONDITIONS.

Authors:  SYLVAIN KOUMLA, RADU PRECUP.
 
       
         
  Abstract:  
DOI: 10.24193/subbmath.2020.1.08

Published Online: 2020-03-06
Published Print: 2020-03-30
pp. 93-108
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ABSTRACT:The paper deals with systems of abstract integrodifferential equations subject to general nonlocal initial conditions. In order to allow the nonlinear terms of the equations to behave independently as much as possible, we use a vector approach based on matrices, vector-valued norms and a vector version of Krasnoselskii''s fixed point theorem for a sum of two operators. The assumptions take into account the support of the nonlocal initial conditions and the hybrid character of the system. Two examples are given to illustrate the theory.

Key words: integrodifferential equation; nonlinear evolution equation; nonlocal initial condition.
 
         
     
         
         
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