Maximal Monotone Differential Inclusions with Volterra and One-Sided Lipschitz Perturbations under Nonlocal Initial Conditions and Applications

Jourani Abderrahim; Torres-Valdebenito Manuel

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arXiv · 2609.27414

Maximal Monotone Differential Inclusions with Volterra and One-Sided Lipschitz Perturbations under Nonlocal Initial Conditions and Applications

Jourani Abderrahim·Torres-Valdebenito Manuel

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Abstract

We investigate a class of differential inclusions governed by non-autonomous and autonomous maximal monotone operators, involving set-valued perturbations with a Volterra integral term and subject to a nonlocal condition. Under suitable assumptions on the governing operator, the set-valued perturbation, and the Volterra kernel, we establish existence results for solutions. In particular, the set-valued perturbation is assumed to satisfy a one-sided Lipschitz condition, while the Volterra kernel is required to be Lipschitz continuous. The existence of a trajectory is established by means of an iterative construction and an application of Zorn's lemma. Finally, several examples are presented to illustrate the applicability of the abstract results.

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BibTeX RIS

Jourani Abderrahim, Torres-Valdebenito Manuel. 2026-09-23. Maximal Monotone Differential Inclusions with Volterra and One-Sided Lipschitz Perturbations under Nonlocal Initial Conditions and Applications. https://arxiv.org/abs/2609.27414

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