Solving Becker’s Problem on Periodic Solutions of Parabolic Evolution Equations
We present existence and multiplicity theorems for periodic mild solutions to parabolic evolution equations. Their peculiarity is a link with the spectrum of the generator of the semigroup rather than with the spectrum of the linearized periodic BVP for the evolution equation. They provide a positiv...
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| Format: | Article |
| Language: | English |
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De Gruyter
2018-04-01
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| Series: | Advanced Nonlinear Studies |
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| Online Access: | https://doi.org/10.1515/ans-2017-6047 |
| _version_ | 1798043384745558016 |
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| author | Vidossich Giovanni |
| author_facet | Vidossich Giovanni |
| author_sort | Vidossich Giovanni |
| collection | DOAJ |
| description | We present existence and multiplicity theorems for periodic mild solutions to parabolic evolution equations. Their peculiarity is a link with the spectrum of the generator of the semigroup rather than with the spectrum of the linearized periodic BVP for the evolution equation. They provide a positive solution to the open problem risen by Becker [3], they extend some results of Castro and Lazer [5] from scalar to systems of parabolic equations, and they are new even for finite-dimensional ODEs. |
| first_indexed | 2024-04-11T22:49:15Z |
| format | Article |
| id | doaj.art-af50c6117e174ccc866f88a33f864124 |
| institution | Directory Open Access Journal |
| issn | 1536-1365 2169-0375 |
| language | English |
| last_indexed | 2024-04-11T22:49:15Z |
| publishDate | 2018-04-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Advanced Nonlinear Studies |
| spelling | doaj.art-af50c6117e174ccc866f88a33f8641242022-12-22T03:58:39ZengDe GruyterAdvanced Nonlinear Studies1536-13652169-03752018-04-0118219521510.1515/ans-2017-6047Solving Becker’s Problem on Periodic Solutions of Parabolic Evolution EquationsVidossich Giovanni0SISSA, Via Bonomea 265, 34136Trieste, ItalyWe present existence and multiplicity theorems for periodic mild solutions to parabolic evolution equations. Their peculiarity is a link with the spectrum of the generator of the semigroup rather than with the spectrum of the linearized periodic BVP for the evolution equation. They provide a positive solution to the open problem risen by Becker [3], they extend some results of Castro and Lazer [5] from scalar to systems of parabolic equations, and they are new even for finite-dimensional ODEs.https://doi.org/10.1515/ans-2017-6047compact semigroupsspectral propertiestopological degreeperiodic solutions,parabolic equationsodes47d60 35k55 34b15 |
| spellingShingle | Vidossich Giovanni Solving Becker’s Problem on Periodic Solutions of Parabolic Evolution Equations Advanced Nonlinear Studies compact semigroups spectral properties topological degree periodic solutions,parabolic equations odes 47d60 35k55 34b15 |
| title | Solving Becker’s Problem on Periodic Solutions of Parabolic Evolution Equations |
| title_full | Solving Becker’s Problem on Periodic Solutions of Parabolic Evolution Equations |
| title_fullStr | Solving Becker’s Problem on Periodic Solutions of Parabolic Evolution Equations |
| title_full_unstemmed | Solving Becker’s Problem on Periodic Solutions of Parabolic Evolution Equations |
| title_short | Solving Becker’s Problem on Periodic Solutions of Parabolic Evolution Equations |
| title_sort | solving becker s problem on periodic solutions of parabolic evolution equations |
| topic | compact semigroups spectral properties topological degree periodic solutions,parabolic equations odes 47d60 35k55 34b15 |
| url | https://doi.org/10.1515/ans-2017-6047 |
| work_keys_str_mv | AT vidossichgiovanni solvingbeckersproblemonperiodicsolutionsofparabolicevolutionequations |