One Sided Lipschitz Evolution Inclusions in Banach Spaces

Ali N. A. Koam, Tzanko Donchev, Alina I. Lazu, Muhammad Rafaqat and Ali Ahmad
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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

Mathematics, 2021, vol. 9, issue 24, 1-15

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.

Keywords: one sided Lipschitz; limit solutions; nonlocal problems (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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