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    STUDIA MATHEMATICA - Issue no. 1 / 2017  
         
  Article:   AN EXISTENCE THEOREM FOR A NON-AUTONOMOUS SECOND ORDER NONLOCAL MULTIVALUED PROBLEM.

Authors:  .
 
       
         
  Abstract:  DOI: https://doi.org/10.24193/subbmath.2017.0008
Published Online: 2017-03-03
Published Print: 2017-03-31


VIEW PDF: AN EXISTENCE THEOREM FOR A NON-AUTONOMOUS SECOND ORDER NONLOCAL MULTIVALUED PROBLEM

In this paper we prove the existence of mild solutions for a nonlocal problem governed by an abstract semilinear non-autonomous second order differential inclusion, where the non-linear part is an upper-Caratheodory semicontinuous multimap. Our existence theorem is obtained thanks to the introduction of a fundamental Cauchy operator. Finally we apply our main result to provide the controllability of a problem involving a non-autonomous wave equation.

Mathematics Subject Classification (2010): 34A60, 34G25.

Keywords: Nonlocal conditions, semilinear non-autonomous second order differential inclusion, fundamental Cauchy operator, fundamental system.
 
         
     
         
         
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