Necessary Optimality Conditions for Higher-Order Infinite Horizon Variational Problems on Time Scales

TL;DR

This paper derives new Euler-Lagrange and transversality optimality conditions for higher-order infinite horizon variational problems on time scales, unifying and extending classical results in continuous and discrete cases.

Contribution

It introduces improved necessary optimality conditions for higher-order infinite horizon variational problems on arbitrary time scales, applicable to both continuous and discrete settings.

Findings

New optimality conditions for time scales

Unification of continuous and discrete cases

Enhanced classical variational results

Abstract

We obtain Euler-Lagrange and transversality optimality conditions for higher-order infinite horizon variational problems on a time scale. The new necessary optimality conditions improve the classical results both in the continuous and discrete settings: our results seem new and interesting even in the particular cases when the time scale is the set of real numbers or the set of integers.