Necessary condition for an Euler-Lagrange equation on time scales
arXiv:1403.3252 · doi:10.1155/2014/631281
Abstract
We prove a necessary condition for a dynamic integro-differential 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.
This is a preprint of a paper whose final and definite form is: Abstract and Applied Analysis 2014, Article ID 631281, http://dx.doi.org/10.1155/2014/631281
References in corpus (10)
- Discrete-Time Fractional Variational Problems
- Calculus of Variations on Time Scales with Nabla Derivatives
- Isoperimetric problems on time scales with nabla derivatives
- Optimality conditions for the calculus of variations with higher-order delta derivatives
- Differential, integral, and variational delta-embeddings of Lagrangian systems
- Higher-order infinite horizon variational problems in discrete quantum calculus
- The Delta-nabla Calculus of Variations for Composition Functionals on Time Scales
- A Time-Scale Variational Approach to Inflation, Unemployment and Social Loss
- Necessary optimality conditions for the calculus of variations on time scales
- Necessary optimality conditions for infinite horizon variational problems on time scales