Necessary Condition for an Euler-Lagrange Equation on Time Scales
We prove a necessary condition for a dynamic integrodifferential equation to be an Euler-Lagrange equation. New and interesting results for the discrete and quantum calculus are obtained as particular cases. An example of a second order dynamic equation, which is not an Euler-Lagrange equation on an...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/631281 |
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| _version_ | 1832545569324662784 |
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| author | Monika Dryl Delfim F. M. Torres |
| author_facet | Monika Dryl Delfim F. M. Torres |
| author_sort | Monika Dryl |
| collection | DOAJ |
| description | We prove a necessary condition for a dynamic integrodifferential equation
to be an Euler-Lagrange equation. New and interesting results for the discrete
and quantum calculus are obtained as particular cases. An example of a second
order dynamic equation, which is not an Euler-Lagrange equation
on an arbitrary time scale, is given. |
| format | Article |
| id | doaj-art-457f5312ce30497faf28efad71dcff06 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-457f5312ce30497faf28efad71dcff062025-02-03T07:25:21ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/631281631281Necessary Condition for an Euler-Lagrange Equation on Time ScalesMonika Dryl0Delfim F. M. Torres1Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, 3810-193 Aveiro, PortugalCenter for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, 3810-193 Aveiro, PortugalWe prove a necessary condition for a dynamic integrodifferential equation to be an Euler-Lagrange equation. New and interesting results for the discrete and quantum calculus are obtained as particular cases. An example of a second order dynamic equation, which is not an Euler-Lagrange equation on an arbitrary time scale, is given.http://dx.doi.org/10.1155/2014/631281 |
| spellingShingle | Monika Dryl Delfim F. M. Torres Necessary Condition for an Euler-Lagrange Equation on Time Scales Abstract and Applied Analysis |
| title | Necessary Condition for an Euler-Lagrange Equation on Time Scales |
| title_full | Necessary Condition for an Euler-Lagrange Equation on Time Scales |
| title_fullStr | Necessary Condition for an Euler-Lagrange Equation on Time Scales |
| title_full_unstemmed | Necessary Condition for an Euler-Lagrange Equation on Time Scales |
| title_short | Necessary Condition for an Euler-Lagrange Equation on Time Scales |
| title_sort | necessary condition for an euler lagrange equation on time scales |
| url | http://dx.doi.org/10.1155/2014/631281 |
| work_keys_str_mv | AT monikadryl necessaryconditionforaneulerlagrangeequationontimescales AT delfimfmtorres necessaryconditionforaneulerlagrangeequationontimescales |