Evolution Inclusions in Banach Spaces under Dissipative Conditions
We develop a new concept of a solution, called the limit solution, to fully nonlinear differential inclusions in Banach spaces. That enables us to study such kind of inclusions under relatively weak conditions. Namely we prove the existence of this type of solutions and some qualitative properties,...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-05-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/8/5/750 |
| _version_ | 1797568489134751744 |
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| author | Tzanko Donchev Shamas Bilal Ovidiu Cârjă Nasir Javaid Alina I. Lazu |
| author_facet | Tzanko Donchev Shamas Bilal Ovidiu Cârjă Nasir Javaid Alina I. Lazu |
| author_sort | Tzanko Donchev |
| collection | DOAJ |
| description | We develop a new concept of a solution, called the limit solution, to fully nonlinear differential inclusions in Banach spaces. That enables us to study such kind of inclusions under relatively weak conditions. Namely we prove the existence of this type of solutions and some qualitative properties, replacing the commonly used compact or Lipschitz conditions by a dissipative one, i.e., one-sided Perron condition. Under some natural assumptions we prove that the set of limit solutions is the closure of the set of integral solutions. |
| first_indexed | 2024-03-10T19:56:37Z |
| format | Article |
| id | doaj.art-980715690fdd4b03a93a5fcb799771b9 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T19:56:37Z |
| publishDate | 2020-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-980715690fdd4b03a93a5fcb799771b92023-11-19T23:53:26ZengMDPI AGMathematics2227-73902020-05-018575010.3390/math8050750Evolution Inclusions in Banach Spaces under Dissipative ConditionsTzanko Donchev0Shamas Bilal1Ovidiu Cârjă2Nasir Javaid3Alina I. Lazu4Department of Mathematics, University of Architecture, Civil Engineering and Geodesy, Sofia 1164, BulgariaDepartment of Mathematics, University of Sialkot, Sialkot 51040, PakistanDepartment of Mathematics, “Al. I. Cuza” University, Iaşi 700506, RomaniaAbdus Salam School of Mathematical Sciences, Lahore 54000, PakistanDepartment of Mathematics, “Gh. Asachi” Technical University, Iaşi 700506, RomaniaWe develop a new concept of a solution, called the limit solution, to fully nonlinear differential inclusions in Banach spaces. That enables us to study such kind of inclusions under relatively weak conditions. Namely we prove the existence of this type of solutions and some qualitative properties, replacing the commonly used compact or Lipschitz conditions by a dissipative one, i.e., one-sided Perron condition. Under some natural assumptions we prove that the set of limit solutions is the closure of the set of integral solutions.https://www.mdpi.com/2227-7390/8/5/750m-dissipative operatorslimit solutionsintegral solutionsone-sided Perron conditionBanach spaces |
| spellingShingle | Tzanko Donchev Shamas Bilal Ovidiu Cârjă Nasir Javaid Alina I. Lazu Evolution Inclusions in Banach Spaces under Dissipative Conditions Mathematics m-dissipative operators limit solutions integral solutions one-sided Perron condition Banach spaces |
| title | Evolution Inclusions in Banach Spaces under Dissipative Conditions |
| title_full | Evolution Inclusions in Banach Spaces under Dissipative Conditions |
| title_fullStr | Evolution Inclusions in Banach Spaces under Dissipative Conditions |
| title_full_unstemmed | Evolution Inclusions in Banach Spaces under Dissipative Conditions |
| title_short | Evolution Inclusions in Banach Spaces under Dissipative Conditions |
| title_sort | evolution inclusions in banach spaces under dissipative conditions |
| topic | m-dissipative operators limit solutions integral solutions one-sided Perron condition Banach spaces |
| url | https://www.mdpi.com/2227-7390/8/5/750 |
| work_keys_str_mv | AT tzankodonchev evolutioninclusionsinbanachspacesunderdissipativeconditions AT shamasbilal evolutioninclusionsinbanachspacesunderdissipativeconditions AT ovidiucarja evolutioninclusionsinbanachspacesunderdissipativeconditions AT nasirjavaid evolutioninclusionsinbanachspacesunderdissipativeconditions AT alinailazu evolutioninclusionsinbanachspacesunderdissipativeconditions |