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...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2014-01-01
|
| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/631281 |
| id |
doaj-457f5312ce30497faf28efad71dcff06 |
|---|---|
| record_format |
Article |
| spelling |
doaj-457f5312ce30497faf28efad71dcff062020-11-24T22:01:59ZengHindawi LimitedAbstract 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 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Monika Dryl Delfim F. M. Torres |
| spellingShingle |
Monika Dryl Delfim F. M. Torres Necessary Condition for an Euler-Lagrange Equation on Time Scales Abstract and Applied Analysis |
| author_facet |
Monika Dryl Delfim F. M. Torres |
| author_sort |
Monika Dryl |
| title |
Necessary Condition for an Euler-Lagrange Equation on Time Scales |
| title_short |
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_sort |
necessary condition for an euler-lagrange equation on time scales |
| publisher |
Hindawi Limited |
| series |
Abstract and Applied Analysis |
| issn |
1085-3375 1687-0409 |
| publishDate |
2014-01-01 |
| 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. |
| url |
http://dx.doi.org/10.1155/2014/631281 |
| work_keys_str_mv |
AT monikadryl necessaryconditionforaneulerlagrangeequationontimescales AT delfimfmtorres necessaryconditionforaneulerlagrangeequationontimescales |
| _version_ |
1725837541076107264 |