Calculus of variations on time scales with nabla derivatives

2008/07/16 by Natália Martins, Natalia Martins, Delfim F. M. Torres · 2 citations
Mathematics · #Applied mathematics #Calculus (dental) #Calculus of variations #Differential Equations and Boundary Problems #Differential Equations and Numerical Methods #Euler's formula #Euler–Lagrange equation #Lagrangian #Lemma (botany) #Mathematical analysis #Mathematics #Nabla symbol #Nonlinear Differential Equations Analysis #Omega #Physics #Pure mathematics #math.CA #math.OC #msc:39A12 #msc:49K05

paper · pdf · doi:10.1016/j.na.2008.11.035

published as Nonlinear Anal. 71 (2009), no. 12, e763--e773 · Partially presented at the Fifth World Congress of Nonlinear Analysts (WCNA-2008), Orlando, Florida, July 2-9, 2008

arxiv created 2008/07/16 · openalex publication_date 2008/11/13 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We prove a necessary optimality condition of Euler-Lagrange type for variational problems on time scales involving nabla derivatives of higher-order. The proof is done using a new and more general fundamental lemma of the calculus of variations on time scales.

Citations

• Noether's theorem on time scales
• Higher-Order Calculus of Variations on Time Scales

Cited by

• Generalizing the variational theory on time scales to include the delta indefinite integral
• Delta-nabla optimal control problems