An existence theorem for a non-autonomous second order nonlocal multivalued problem

Tiziana Cardinali, Serena Gentili

Abstract


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.

Keywords


nonlocal conditions; semilinear non-autonomous second order differential inclusion; fundamental Cauchy operator; fundamental system

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References


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DOI: http://dx.doi.org/10.24193/subbmath.2017.0008

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