Isoperimetric Problems of the Calculus of Variations on Time Scales

TL;DR

This paper establishes a necessary optimality condition for isoperimetric problems within the calculus of variations on time scales and applies it to Sturm-Liouville eigenvalue problems, bridging continuous and discrete analysis.

Contribution

It introduces a new optimality condition for isoperimetric problems on time scales and demonstrates its application to Sturm-Liouville eigenvalue problems.

Findings

Derived a necessary optimality condition for isoperimetric problems on time scales.

Applied the condition to Sturm-Liouville eigenvalue problems on time scales.

Bridged continuous and discrete calculus of variations through time scales.

Abstract

We prove a necessary optimality condition for isoperimetric problems on time scales in the space of delta-differentiable functions with rd-continuous derivatives. The results are then applied to Sturm-Liouville eigenvalue problems on time scales.