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Evolution Inclusions in Banach Spaces under Dissipative Conditions

Author

Listed:
  • 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
    “Octav Mayer” Mathematics Institute, Romanian Academy, Iaşi 700505, 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)

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.

Suggested Citation

  • Tzanko Donchev & Shamas Bilal & Ovidiu Cârjă & Nasir Javaid & Alina I. Lazu, 2020. "Evolution Inclusions in Banach Spaces under Dissipative Conditions," Mathematics, MDPI, vol. 8(5), pages 1-17, May.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:5:p:750-:d:355785
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