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Title: Direct and inverse variational problems on time scales: A survey
Author: Dryl, M.
Torres, D. F. M.
Keywords: Calculus of variations
Dynamic equations on time scales
Equation of variation
Helmholtz’s problem
Inverse problems
Self-adjoint equations
Issue Date: 2017
Publisher: Springer
Abstract: We deal with direct and inverse problems of the calculus of variations on arbitrary time scales. Firstly, using the Euler–Lagrange equation and the strengthened Legendre condition, we give a general form for a variational functional to attain a local minimum at a given point of the vector space. Furthermore, we provide a necessary condition for a dynamic integro-differential equation to be an Euler–Lagrange equation (Helmholtz’s problem of the calculus of variations on time scales). New and interesting results for the discrete and quantum settings are obtained as particular cases. Finally, we consider very general problems of the calculus of variations given by the composition of a certain scalar function with delta and nabla integrals of a vector valued field. © 2017, Springer International Publishing AG.
Peer review: yes
DOI: 10.1007/978-3-319-55236-1_12
ISSN: 2194-1009
Appears in Collections:CIDMA - Artigos
SCG - Artigos

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