Evolution Inclusions in Banach Spaces under Dissipative Conditions

Tzanko Donchev, Shamas Bilal, Ovidiu Cârjă, Nasir Javaid and Alina I. Lazu
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Tzanko Donchev: Department of Mathematics, University of Architecture, Civil Engineering and Geodesy, Sofia 1164, Bulgaria
Shamas Bilal: Department of Mathematics, University of Sialkot, Sialkot 51040, Pakistan
Ovidiu Cârjă: Department of Mathematics, “Al. I. Cuza” University, Iaşi 700506, Romania
Nasir Javaid: Abdus Salam School of Mathematical Sciences, Lahore 54000, Pakistan
Alina I. Lazu: Department of Mathematics, “Gh. Asachi” Technical University, Iaşi 700506, Romania

Mathematics, 2020, vol. 8, issue 5, 1-17

Abstract: We develop a new concept of a solution, called the limit solution, to fully nonlinear differential inclusions in Banach spaces. That enables us to study such kind of inclusions under relatively weak conditions. Namely we prove the existence of this type of solutions and some qualitative properties, replacing the commonly used compact or Lipschitz conditions by a dissipative one, i.e., one-sided Perron condition. Under some natural assumptions we prove that the set of limit solutions is the closure of the set of integral solutions.

Keywords: m-dissipative operators; limit solutions; integral solutions; one-sided Perron condition; Banach spaces (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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