Existence of positive periodic solutions for evolution equations with delay in ordered Banach spaces
The main focus of this study is to discuss the existence of positive ω\omega -periodic mild solutions for evolution equation with delay in an ordered Banach space EE. Under the ordered conditions of the growth exponent of the nonlinearity gg with respect to the semigroup T(t)(t≥0){\mathcal{T}}\left(...
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De Gruyter
2025-06-01
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| Series: | Open Mathematics |
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| Online Access: | https://doi.org/10.1515/math-2025-0165 |
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| author | Zhang Jing Gou Haide |
| author_facet | Zhang Jing Gou Haide |
| author_sort | Zhang Jing |
| collection | DOAJ |
| description | The main focus of this study is to discuss the existence of positive ω\omega -periodic mild solutions for evolution equation with delay in an ordered Banach space EE. Under the ordered conditions of the growth exponent of the nonlinearity gg with respect to the semigroup T(t)(t≥0){\mathcal{T}}\left(t)\hspace{.25em}\left(t\ge 0) or the first eigenvalue of the operator A{\mathcal{A}}, the existence results of mild solutions and positive mild solutions for evolution equation are obtained by applying the Poincaré mapping and monotone iterative method, and adding appropriate conditions to the nonlinearity term gg without assuming the existence of upper and lower solutions. Finally, we give an example to verify the applicability of our abstract results. |
| format | Article |
| id | doaj-art-8c97ba2b53b74a84bed7e9ef261aaf80 |
| institution | OA Journals |
| issn | 2391-5455 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Open Mathematics |
| spelling | doaj-art-8c97ba2b53b74a84bed7e9ef261aaf802025-08-20T02:38:15ZengDe GruyterOpen Mathematics2391-54552025-06-0123117719710.1515/math-2025-0165Existence of positive periodic solutions for evolution equations with delay in ordered Banach spacesZhang Jing0Gou Haide1College of Science, Gansu Agricultural University, Lanzhou, 730070, P. R. ChinaCollege of Mathematics and Statistics, Northwest Normal University, Lanzhou, 730070, P. R. ChinaThe main focus of this study is to discuss the existence of positive ω\omega -periodic mild solutions for evolution equation with delay in an ordered Banach space EE. Under the ordered conditions of the growth exponent of the nonlinearity gg with respect to the semigroup T(t)(t≥0){\mathcal{T}}\left(t)\hspace{.25em}\left(t\ge 0) or the first eigenvalue of the operator A{\mathcal{A}}, the existence results of mild solutions and positive mild solutions for evolution equation are obtained by applying the Poincaré mapping and monotone iterative method, and adding appropriate conditions to the nonlinearity term gg without assuming the existence of upper and lower solutions. Finally, we give an example to verify the applicability of our abstract results.https://doi.org/10.1515/math-2025-0165monotone iterative methodperiodic solutionscompact semigrouppoincaré mappingpositive c 0-semigroupevolution equations with delay34g1034k4547d0334k3047h0747h08 |
| spellingShingle | Zhang Jing Gou Haide Existence of positive periodic solutions for evolution equations with delay in ordered Banach spaces Open Mathematics monotone iterative method periodic solutions compact semigroup poincaré mapping positive c 0-semigroup evolution equations with delay 34g10 34k45 47d03 34k30 47h07 47h08 |
| title | Existence of positive periodic solutions for evolution equations with delay in ordered Banach spaces |
| title_full | Existence of positive periodic solutions for evolution equations with delay in ordered Banach spaces |
| title_fullStr | Existence of positive periodic solutions for evolution equations with delay in ordered Banach spaces |
| title_full_unstemmed | Existence of positive periodic solutions for evolution equations with delay in ordered Banach spaces |
| title_short | Existence of positive periodic solutions for evolution equations with delay in ordered Banach spaces |
| title_sort | existence of positive periodic solutions for evolution equations with delay in ordered banach spaces |
| topic | monotone iterative method periodic solutions compact semigroup poincaré mapping positive c 0-semigroup evolution equations with delay 34g10 34k45 47d03 34k30 47h07 47h08 |
| url | https://doi.org/10.1515/math-2025-0165 |
| work_keys_str_mv | AT zhangjing existenceofpositiveperiodicsolutionsforevolutionequationswithdelayinorderedbanachspaces AT gouhaide existenceofpositiveperiodicsolutionsforevolutionequationswithdelayinorderedbanachspaces |