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    STUDIA MATHEMATICA - Issue no. 3 / 2009  
         
  Article:   FIRST ORDER FUNCTIONAL DIFFERENTIAL EQUATIONS WITH STATE-DEPENDENT MODIFIED ARGUMENT.

Authors:  EDITH EGRI, IOAN A. RUS.
 
       
         
  Abstract:  The aim of our paper is to investigate the Cauchy problem constituting from the first order functional differential equation with state-dependent modified argument of the following form  where  and the associated generalized initial value  We look for the solutions of the mentioned problem and deal with its properties, searching conditions for its existence and uniqueness, studying the data dependence: continuity, Lipschitz-continuity and differentiability regarding a parameter.

Keywords and phrases. Iterative functional differential equations, state dependent modified argument, Cauchy problem, contraction principle, Schauder fixed point theorem, data dependence.
 
         
     
         
         
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