The Existence of Periodic Solutions of Delay Differential Equations by E+-Conley Index Theory
In this paper, the E+-Conley index theory has been used to study the existence of periodic solutions of nonautonomous delay differential equations (in short, DDEs). The variational structure for DDEs is built, and the existence of periodic solutions of DDEs is transferred to that of critical points...
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2022/3396716 |
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| _version_ | 1832550790044057600 |
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| author | Huafeng Xiao |
| author_facet | Huafeng Xiao |
| author_sort | Huafeng Xiao |
| collection | DOAJ |
| description | In this paper, the E+-Conley index theory has been used to study the existence of periodic solutions of nonautonomous delay differential equations (in short, DDEs). The variational structure for DDEs is built, and the existence of periodic solutions of DDEs is transferred to that of critical points of the associated function. When DDEs are 2π-nonresonant, some sufficient conditions are obtained to guarantee the existence of periodic solutions. When the system is 2π-resonant at infinity, by making use a second disturbing of the original functional, some sufficient conditions are obtained to guarantee the existence of periodic solutions to DDEs. |
| format | Article |
| id | doaj-art-58e278d5d71b4dd39bb928ad7e8ccee5 |
| institution | Kabale University |
| issn | 2314-8888 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-58e278d5d71b4dd39bb928ad7e8ccee52025-02-03T06:05:50ZengWileyJournal of Function Spaces2314-88882022-01-01202210.1155/2022/3396716The Existence of Periodic Solutions of Delay Differential Equations by E+-Conley Index TheoryHuafeng Xiao0School of Mathematics and Information ScienceIn this paper, the E+-Conley index theory has been used to study the existence of periodic solutions of nonautonomous delay differential equations (in short, DDEs). The variational structure for DDEs is built, and the existence of periodic solutions of DDEs is transferred to that of critical points of the associated function. When DDEs are 2π-nonresonant, some sufficient conditions are obtained to guarantee the existence of periodic solutions. When the system is 2π-resonant at infinity, by making use a second disturbing of the original functional, some sufficient conditions are obtained to guarantee the existence of periodic solutions to DDEs.http://dx.doi.org/10.1155/2022/3396716 |
| spellingShingle | Huafeng Xiao The Existence of Periodic Solutions of Delay Differential Equations by E+-Conley Index Theory Journal of Function Spaces |
| title | The Existence of Periodic Solutions of Delay Differential Equations by E+-Conley Index Theory |
| title_full | The Existence of Periodic Solutions of Delay Differential Equations by E+-Conley Index Theory |
| title_fullStr | The Existence of Periodic Solutions of Delay Differential Equations by E+-Conley Index Theory |
| title_full_unstemmed | The Existence of Periodic Solutions of Delay Differential Equations by E+-Conley Index Theory |
| title_short | The Existence of Periodic Solutions of Delay Differential Equations by E+-Conley Index Theory |
| title_sort | existence of periodic solutions of delay differential equations by e conley index theory |
| url | http://dx.doi.org/10.1155/2022/3396716 |
| work_keys_str_mv | AT huafengxiao theexistenceofperiodicsolutionsofdelaydifferentialequationsbyeconleyindextheory AT huafengxiao existenceofperiodicsolutionsofdelaydifferentialequationsbyeconleyindextheory |