Boundary Value Problems for Systems of Second-Order Dynamic Equations on Time Scales with Δ-Carathéodory Functions
We establish the existence of solutions to systems of second-order dynamic equations on time scales with the right member f, a Δ-Carathéodory function. First, we consider the case where the nonlinearity f does not depend on the Δ-derivative, xΔ(t). We obtain existence results for Strum-Liouville and...
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| Format: | Article |
| Language: | English |
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Wiley
2010-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2010/234015 |
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| _version_ | 1832561298632605696 |
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| author | M. Frigon H. Gilbert |
| author_facet | M. Frigon H. Gilbert |
| author_sort | M. Frigon |
| collection | DOAJ |
| description | We establish the existence of solutions to systems of second-order dynamic equations on time scales with the right member f, a Δ-Carathéodory function. First, we consider the case where the nonlinearity f does not depend on the Δ-derivative, xΔ(t). We obtain existence results for Strum-Liouville and for periodic boundary conditions. Finally, we consider more general systems
in which the nonlinearity f depends on the Δ-derivative and satisfies a linear growth condition with respect to xΔ(t). Our existence results rely on notions of solution-tube that are introduced in this paper. |
| format | Article |
| id | doaj-art-8ddee16bb2e44f3fa3d35abcdc512f9a |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2010-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-8ddee16bb2e44f3fa3d35abcdc512f9a2025-02-03T01:25:30ZengWileyAbstract and Applied Analysis1085-33751687-04092010-01-01201010.1155/2010/234015234015Boundary Value Problems for Systems of Second-Order Dynamic Equations on Time Scales with Δ-Carathéodory FunctionsM. Frigon0H. Gilbert1Département de Mathématiques et de Statistique, Université de Montréal, CP 6128, Succursale Centre-Ville, Montréal, QC, H3C 3J7, CanadaDépartement de Mathématiques, Collège Édouard-Montpetit, 945 Chemin de Chambly, Longueuil, QC, J4H 3M6, CanadaWe establish the existence of solutions to systems of second-order dynamic equations on time scales with the right member f, a Δ-Carathéodory function. First, we consider the case where the nonlinearity f does not depend on the Δ-derivative, xΔ(t). We obtain existence results for Strum-Liouville and for periodic boundary conditions. Finally, we consider more general systems in which the nonlinearity f depends on the Δ-derivative and satisfies a linear growth condition with respect to xΔ(t). Our existence results rely on notions of solution-tube that are introduced in this paper.http://dx.doi.org/10.1155/2010/234015 |
| spellingShingle | M. Frigon H. Gilbert Boundary Value Problems for Systems of Second-Order Dynamic Equations on Time Scales with Δ-Carathéodory Functions Abstract and Applied Analysis |
| title | Boundary Value Problems for Systems of Second-Order Dynamic Equations on Time Scales with Δ-Carathéodory Functions |
| title_full | Boundary Value Problems for Systems of Second-Order Dynamic Equations on Time Scales with Δ-Carathéodory Functions |
| title_fullStr | Boundary Value Problems for Systems of Second-Order Dynamic Equations on Time Scales with Δ-Carathéodory Functions |
| title_full_unstemmed | Boundary Value Problems for Systems of Second-Order Dynamic Equations on Time Scales with Δ-Carathéodory Functions |
| title_short | Boundary Value Problems for Systems of Second-Order Dynamic Equations on Time Scales with Δ-Carathéodory Functions |
| title_sort | boundary value problems for systems of second order dynamic equations on time scales with δ caratheodory functions |
| url | http://dx.doi.org/10.1155/2010/234015 |
| work_keys_str_mv | AT mfrigon boundaryvalueproblemsforsystemsofsecondorderdynamicequationsontimescaleswithdcaratheodoryfunctions AT hgilbert boundaryvalueproblemsforsystemsofsecondorderdynamicequationsontimescaleswithdcaratheodoryfunctions |