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
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- A Time-Scale Variational Approach to Inflation, Unemployment and Social Loss
- Direct and Inverse Variational Problems on Time Scales: A Survey
- Nondifferentiable variational principles in terms of a quantum operator
- An Inverse Problem of the Calculus of Variations on Arbitrary Time Scales
- Existence of Three Positive Solutions to Some -Laplacian Boundary Value Problems
- Necessary optimality conditions for infinite horizon variational problems on time scales