Integral Inequalities and their Applications to the Calculus of Variations on Time Scales

TL;DR

This paper explores how integral inequalities can be utilized to solve variational problems within the calculus of variations on time scales, unifying continuous and discrete analysis.

Contribution

It introduces new methods leveraging inequalities to address variational problems on time scales, bridging continuous and discrete calculus.

Findings

Derived new integral inequalities for time scales

Applied inequalities to solve specific variational problems

Unified approach for continuous and discrete variational calculus

Abstract

We discuss the use of inequalities to obtain the solution of certain variational problems on time scales.