Generalizing the variational theory on time scales to include the delta indefinite integral
arXiv:1102.3727 · doi:10.1016/j.camwa.2011.02.022
Abstract
We prove necessary optimality conditions of Euler-Lagrange type for generalized problems of the calculus of variations on time scales with a Lagrangian depending not only on the independent variable, an unknown function and its delta derivative, but also on a delta indefinite integral that depends on the unknown function. Such kind of variational problems were considered by Euler himself and have been recently investigated in [Methods Appl. Anal. 15 (2008), no. 4, 427-435]. Our results not only provide a generalization to previous results, but also give some other interesting optimality conditions as special cases.
Submitted 25-Jul-2010; revised 27-Nov-2010; accepted 16-Feb-2011; for publication in Computers and Mathematics with Applications
References in corpus (7)
- Calculus of Variations on Time Scales with Nabla Derivatives
- Transversality Conditions for Infinite Horizon Variational Problems on Time Scales
- The Hahn Quantum Variational Calculus
- Isoperimetric problems on time scales with nabla derivatives
- The Second Euler-Lagrange Equation of Variational Calculus on Time Scales
- Noether's symmetry theorem for nabla problems of the calculus of variations
- Backward Linear Control Systems on Time Scales