- PII
- 10.31857/S268695432360012X-1
- DOI
- 10.31857/S268695432360012X
- Publication type
- Status
- Published
- Authors
- Volume/ Edition
- Volume 514 / Issue number 1
- Pages
- 65-68
- Abstract
- 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.
- Keywords
- максимально монотонный оператор <span class="inline-formula"><span class="math">\(\rho \)</span></span>-полуотклонение операторов релаксация
- Date of publication
- 01.01.2023
- Year of publication
- 2023
- Number of purchasers
- 0
- Views
- 41
References
- 1. Vladimirov A.A. Nonstationary dissipative evolution equations in a Hilbert space // Nonlinear Anal. 1991. V. 17. P. 499–518. https://doi.org/10.1016/0362-546X (91)90061-5
- 2. Azzam-Laouir D., Belhoula W., Castaing C., Monteiro Marques M.D.P. Perturbed evolution problems with absolutely continuous variation in time and applications // J. Fixed Point Theory. Appl. 2019. V. 21. 40. https://doi.org/10.1007/s11784-019-0666-2
- 3. Azzam-Laouir D., Boutana Harid I. Mixed semicontinuous perturbation to an evolution problem with time-dependent maximal monotone operator // J. Nonlinear Convex Anal. 2019. V. 20. № 1. P. 35–92.
- 4. Azzam-Laouir D., Belhoula W., Castaing C., Monteiro Marques M.D.P. Multivalued perturbation to evolution problems involving time dependent maximal monotone operators // Evolution Equations and Control Theory. 2019. V. 9. № 1. P. 219–254. https://doi.org/10.3934/eect.2020004
- 5. Castaing Ch., Saidi S. Lipschitz perturbation to evolution inclusions driven by time-dependent maximal monotone operators // Topol. Math. Nonlinear Anal. 2021. V. 58. № 2. P. 677–712. https://doi.org/10.12775/TMNA.2021.012
- 6. Tolstonogov A.A. Existence and relaxation of solutions for a subdifferential inclusion with unbounded perturbation // J. Math. Anal. Appl. 2017. V. 447. P. 269–288. https://doi.org/10.1016/j.jmaa.2016.09.061
- 7. Tolstonogov A.A. Sweeping process with unbounded nonconvex perturbation // Nonlinear Analysis. 2014. V. 108. P. 291–301. https://doi.org/10.1016/j.na.2014.06.002
- 8. Attouch H., Wets R.J.-B. Quantitative stability of variational systems. I: The epigraphical distance // Trans. Amer. Math. Soc. 1991. V. 328. № 2. P. 695–729. https://doi.org/10.2307/2001800
