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Authors: .
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.
