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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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2025-06-01
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| Series: | Open Mathematics |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/math-2025-0161 |
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| Summary: | 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. |
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| ISSN: | 2391-5455 |