Nonlocal problems in Hilbert spaces

Irene  Benedetti; Luisa Malaguti; Valentina  Taddei

doi:10.3934/proc.2015.0103

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2015, Volume 2015: 103-111. Doi: 10.3934/proc.2015.0103 open access

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Nonlocal problems in Hilbert spaces

1.
Department of Mathematics and Informatics, University of Perugia
2.
Dept. of Engineering Sciences and Methods, University of Modena and Reggio Emilia, I-42100
3.
Department of Physics, Informatics and Mathematics, University of Modena and Reggio Emilia

Received: August 31, 2014

Revised: December 31, 2014

Published: October 2015

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Abstract

An existence result for differential inclusions in a separable Hilbert space is furnished. A wide family of nonlocal boundary value problems is treated, including periodic, anti-periodic, mean value and multipoint conditions. The study is based on an approximation solvability method. Advanced topological methods are used as well as a Scorza Dragoni-type result for multivalued maps. The conclusions are original also in the single-valued setting. An application to a nonlocal dispersal model is given.

Keywords:

Mathematics Subject Classification: Primary: 34B10; Secondary: 34A60, 34B15, 49J53.

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