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One Sided Lipschitz Evolution Inclusions in Banach Spaces

Author

Listed:
  • Ali N. A. Koam

    (Department of Mathematics, College of Science, New Campus, Jazan University, Jazan 2097, Saudi Arabia)

  • Tzanko Donchev

    (Department of Mathematics, University of Architecture, Civil Engineering and Geodesy (UACG), 1 Hr. Smirnenski Boulevard, 1046 Sofia, Bulgaria)

  • Alina I. Lazu

    (Department of Mathematics, “Gh. Asachi” Technical University, 700506 Iaşi, Romania)

  • Muhammad Rafaqat

    (Department of Mathematics, University of Lahore, Lahore 53700, Pakistan)

  • Ali Ahmad

    (College of Computer Science and Information Technology, Jazan University, Jazan 45142, Saudi Arabia)

Abstract

Using the notion of limit solution, we study multivalued perturbations of m-dissipative differential inclusions with nonlocal initial conditions. These solutions enable us to work in general Banach spaces, in particular L 1 . The commonly used Lipschitz condition on the right-hand side is weakened to a one-sided Lipschitz one. No compactness assumptions are required. We consider the cases of an arbitrary one-sided Lipschitz condition and the case of a negative one-sided Lipschitz constant. Illustrative examples, which can be modifications of real models, are provided.

Suggested Citation

  • Ali N. A. Koam & Tzanko Donchev & Alina I. Lazu & Muhammad Rafaqat & Ali Ahmad, 2021. "One Sided Lipschitz Evolution Inclusions in Banach Spaces," Mathematics, MDPI, vol. 9(24), pages 1-15, December.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:24:p:3265-:d:703826
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