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Direct and inverse variational problems on time scales: A survey

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Resumo: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.
Autores principais:Dryl, M.
Outros Autores:Torres, D. F. M.
Assunto:Calculus of variations Dynamic equations on time scales Equation of variation Helmholtz’s problem Inverse problems Self-adjoint equations
Ano:2017
País:Portugal
Tipo de documento:artigo
Tipo de acesso:acesso restrito
Instituição associada:Universidade de Aveiro
Idioma:inglês
Origem:RIA - Repositório Institucional da Universidade de Aveiro

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