Existence and multiplicity of positive solutions for multiparameter periodic systems
We deal with the existence and multiplicity of positive solutions for differential systems depending on two parameters, λ1,λ2{\lambda }_{1},{\lambda }_{2}, subjected to periodic boundary conditions. We establish the existence of a continuous curve Γ\Gamma that separates the first quadrant into two...
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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-2025-0161 |
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| author | Wei Liping Dai Yongqiang Su Shunchang |
| author_facet | Wei Liping Dai Yongqiang Su Shunchang |
| author_sort | Wei Liping |
| collection | DOAJ |
| description | We deal with the existence and multiplicity of positive solutions for differential systems depending on two parameters, λ1,λ2{\lambda }_{1},{\lambda }_{2}, subjected to periodic boundary conditions. We establish the existence of a continuous curve Γ\Gamma that separates the first quadrant into two disjoint unbounded open sets O1{{\mathcal{O}}}_{1} and O2{{\mathcal{O}}}_{2}. Specifically, we prove that the periodic system has no positive solutions if (λ1,λ2)∈O1\left({\lambda }_{1},{\lambda }_{2})\in {{\mathcal{O}}}_{1}, at least one positive solution if (λ1,λ2)∈Γ\left({\lambda }_{1},{\lambda }_{2})\in \Gamma , and at least two positive solutions if (λ1,λ2)∈O2\left({\lambda }_{1},{\lambda }_{2})\in {{\mathcal{O}}}_{2}. Our approach relies on the fixed point index theory and the method of lower and upper solutions. |
| format | Article |
| id | doaj-art-e85031f37ee649dcb387b298d4d36fe8 |
| institution | Kabale University |
| issn | 2391-5455 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Open Mathematics |
| spelling | doaj-art-e85031f37ee649dcb387b298d4d36fe82025-08-20T03:28:32ZengDe GruyterOpen Mathematics2391-54552025-06-012311185119710.1515/math-2025-0161Existence and multiplicity of positive solutions for multiparameter periodic systemsWei Liping0Dai Yongqiang1Su Shunchang2College of Information Science and Technology, Gansu Agricultural University, Lanzhou, P. R. ChinaCollege of Information Science and Technology, Gansu Agricultural University, Lanzhou, P. R. ChinaCollege of Information Science and Technology, Gansu Agricultural University, Lanzhou, P. R. ChinaWe deal with the existence and multiplicity of positive solutions for differential systems depending on two parameters, λ1,λ2{\lambda }_{1},{\lambda }_{2}, subjected to periodic boundary conditions. We establish the existence of a continuous curve Γ\Gamma that separates the first quadrant into two disjoint unbounded open sets O1{{\mathcal{O}}}_{1} and O2{{\mathcal{O}}}_{2}. Specifically, we prove that the periodic system has no positive solutions if (λ1,λ2)∈O1\left({\lambda }_{1},{\lambda }_{2})\in {{\mathcal{O}}}_{1}, at least one positive solution if (λ1,λ2)∈Γ\left({\lambda }_{1},{\lambda }_{2})\in \Gamma , and at least two positive solutions if (λ1,λ2)∈O2\left({\lambda }_{1},{\lambda }_{2})\in {{\mathcal{O}}}_{2}. Our approach relies on the fixed point index theory and the method of lower and upper solutions.https://doi.org/10.1515/math-2025-0161positive solutionnon-existence/existenceperiodic systemslower and upper solutions34b1534b18 |
| spellingShingle | Wei Liping Dai Yongqiang Su Shunchang Existence and multiplicity of positive solutions for multiparameter periodic systems Open Mathematics positive solution non-existence/existence periodic systems lower and upper solutions 34b15 34b18 |
| title | Existence and multiplicity of positive solutions for multiparameter periodic systems |
| title_full | Existence and multiplicity of positive solutions for multiparameter periodic systems |
| title_fullStr | Existence and multiplicity of positive solutions for multiparameter periodic systems |
| title_full_unstemmed | Existence and multiplicity of positive solutions for multiparameter periodic systems |
| title_short | Existence and multiplicity of positive solutions for multiparameter periodic systems |
| title_sort | existence and multiplicity of positive solutions for multiparameter periodic systems |
| topic | positive solution non-existence/existence periodic systems lower and upper solutions 34b15 34b18 |
| url | https://doi.org/10.1515/math-2025-0161 |
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