EXISTENCE AND RELAXATION OF SOLUTIONS FOR A DIFFERENTIAL INCLUSION WITH MAXIMAL MONOTONE OPERATORS AND PERTURBATIONS
- Авторлар: Tolstonogov A.1
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Мекемелер:
- Matrosov Institute for System Dynamics and Control Theory of Siberian Branch of Russian Academy of Sciences
- Шығарылым: Том 514, № 1 (2023)
- Беттер: 65-68
- Бөлім: МАТЕМАТИКА
- URL: https://journals.rcsi.science/2686-9543/article/view/247086
- DOI: https://doi.org/10.31857/S268695432360012X
- EDN: https://elibrary.ru/DAUBQA
- ID: 247086
Дәйексөз келтіру
Аннотация
A differential inclusion with a time-dependent maximal monotone operator and a perturbation is studied in a separable Hilbert space. The perturbation is the sum of a time-dependent single-valued operator and a multivalued mapping with closed nonconvex values. A particular feature of the single-valued operator is that its sum its with the identity operator multiplied by a positive square-integrable function is a monotone operator. The multivalued mapping is Lipschitz continuous with respect to the phase variable. We prove the existence of a solution and the density in the corresponding topology of the solution set of the initial inclusion in the solution set of the inclusion with the convexified multivalued mapping. For these purposes, new distances between maximal monotone operators are introduced.
Негізгі сөздер
Авторлар туралы
A. Tolstonogov
Matrosov Institute for System Dynamics and Control Theory of Siberian Branch of Russian Academy of Sciences
Хат алмасуға жауапты Автор.
Email: alexander.tolstonogov@gmail.com
Russian Federation, Irkutsk
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