An Inverse Problem of the Calculus of Variations on Arbitrary Time Scales
arXiv:1401.8232
Abstract
We consider an inverse extremal problem for variational functionals on arbitrary time scales. Using the Euler-Lagrange equation and the strengthened Legendre condition, we derive a general form for a variational functional that attains a local minimum at a given point of the vector space.
This is a preprint of a paper whose final and definite form will appear in International Journal of Difference Equations, ISSN 0973-6069 (See http://campus.mst.edu/ijde). Submitted Nov 27, 2013; Revised Jan 24, 2014; Accepted Jan 31, 2014