Necessary Condition for an Euler-Lagrange Equation on Time Scales-Reference-Cited by-同舟云学术

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Necessary Condition for an Euler-Lagrange Equation on Time Scales

Published:2014 Issue: Volume:2014 Page:1-7
ISSN:1085-3375
Container-title:Abstract and Applied Analysis
language:en
Short-container-title:Abstract and Applied Analysis

Author:

Dryl Monika¹,Torres Delfim F. M.¹

Affiliation:

1. Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal

Abstract

We prove a necessary condition for a dynamic integrodifferential equation to be an Euler-Lagrange equation. New and interesting results for the discrete and quantum calculus are obtained as particular cases. An example of a second order dynamic equation, which is not an Euler-Lagrange equation on an arbitrary time scale, is given.

Publisher

Hindawi Limited

Subject

Applied Mathematics,Analysis

Link

http://downloads.hindawi.com/journals/aaa/2014/631281.pdf

Reference20 articles.

1. Analysis on Measure Chains — A Unified Approach to Continuous and Discrete Calculus

2. Dynamic Equations on Time Scales

3. Dynamic equations on time scales: a survey

4. Advances in Dynamic Equations on Time Scales

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1. Direct and Inverse Variational Problems on Time Scales: A Survey;Modeling, Dynamics, Optimization and Bioeconomics II;2017

2. Helmholtz Theorem for Nondifferentiable Hamiltonian Systems in the Framework of Cresson’s Quantum Calculus;Discrete Dynamics in Nature and Society;2016

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