Nonlocal evolution inclusions under weak conditions
Abstract We study evolution inclusions given by multivalued perturbations of m-dissipative operators with nonlocal initial conditions. We prove the existence of solutions. The commonly used Lipschitz hypothesis for the perturbations is weakened to one-sided Lipschitz ones. We prove an existence resu...
| Main Authors: | , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2018-10-01
|
| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13662-018-1858-6 |
| _version_ | 1818263448773984256 |
|---|---|
| author | Shamas Bilal Ovidiu Cârjă Tzanko Donchev Nasir Javaid Alina I. Lazu |
| author_facet | Shamas Bilal Ovidiu Cârjă Tzanko Donchev Nasir Javaid Alina I. Lazu |
| author_sort | Shamas Bilal |
| collection | DOAJ |
| description | Abstract We study evolution inclusions given by multivalued perturbations of m-dissipative operators with nonlocal initial conditions. We prove the existence of solutions. The commonly used Lipschitz hypothesis for the perturbations is weakened to one-sided Lipschitz ones. We prove an existence result for the multipoint problems that cover periodic and antiperiodic cases. We give examples to illustrate the applicability of our results. |
| first_indexed | 2024-12-12T19:19:11Z |
| format | Article |
| id | doaj.art-4f7eef74491c474f929d1f685aaa9469 |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-12-12T19:19:11Z |
| publishDate | 2018-10-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-4f7eef74491c474f929d1f685aaa94692022-12-22T00:14:40ZengSpringerOpenAdvances in Difference Equations1687-18472018-10-012018111410.1186/s13662-018-1858-6Nonlocal evolution inclusions under weak conditionsShamas Bilal0Ovidiu Cârjă1Tzanko Donchev2Nasir Javaid3Alina I. Lazu4Abdus Salam School of Mathematical Sciences“Octav Mayer” Mathematics Institute, Romanian AcademyDepartment of Mathematics, “Al. I. Cuza” UniversityAbdus Salam School of Mathematical SciencesDepartment of Mathematics, “Gh. Asachi” Technical UniversityAbstract We study evolution inclusions given by multivalued perturbations of m-dissipative operators with nonlocal initial conditions. We prove the existence of solutions. The commonly used Lipschitz hypothesis for the perturbations is weakened to one-sided Lipschitz ones. We prove an existence result for the multipoint problems that cover periodic and antiperiodic cases. We give examples to illustrate the applicability of our results.http://link.springer.com/article/10.1186/s13662-018-1858-6m-dissipative evolution inclusionsNonlocal initial conditionsOne-sided Lipschitz condition |
| spellingShingle | Shamas Bilal Ovidiu Cârjă Tzanko Donchev Nasir Javaid Alina I. Lazu Nonlocal evolution inclusions under weak conditions Advances in Difference Equations m-dissipative evolution inclusions Nonlocal initial conditions One-sided Lipschitz condition |
| title | Nonlocal evolution inclusions under weak conditions |
| title_full | Nonlocal evolution inclusions under weak conditions |
| title_fullStr | Nonlocal evolution inclusions under weak conditions |
| title_full_unstemmed | Nonlocal evolution inclusions under weak conditions |
| title_short | Nonlocal evolution inclusions under weak conditions |
| title_sort | nonlocal evolution inclusions under weak conditions |
| topic | m-dissipative evolution inclusions Nonlocal initial conditions One-sided Lipschitz condition |
| url | http://link.springer.com/article/10.1186/s13662-018-1858-6 |
| work_keys_str_mv | AT shamasbilal nonlocalevolutioninclusionsunderweakconditions AT ovidiucarja nonlocalevolutioninclusionsunderweakconditions AT tzankodonchev nonlocalevolutioninclusionsunderweakconditions AT nasirjavaid nonlocalevolutioninclusionsunderweakconditions AT alinailazu nonlocalevolutioninclusionsunderweakconditions |