Necessary optimality conditions for infinite horizon variational problems on time scales

TL;DR

This paper establishes Euler-Lagrange equations and transversality conditions for infinite horizon variational problems on time scales, accommodating Lagrangians with variable dependencies including nabla derivatives and integrals.

Contribution

It introduces necessary optimality conditions for complex infinite horizon variational problems on time scales with generalized dependencies.

Findings

Derived Euler-Lagrange equations for the problems.

Established transversality conditions at infinity.

Extended calculus of variations to time scales with nabla derivatives and integrals.

Abstract

We prove Euler-Lagrange type equations and transversality conditions for generalized infinite horizon problems of the calculus of variations on time scales. Here the Lagrangian depends on the independent variable, an unknown function and its nabla derivative, as well as a nabla indefinite integral that depends on the unknown function.