Existence of minimizers for generalized Lagrangian functionals and a necessary optimality condition - Application to fractional variational problems
Résumé
We study dynamic minimization problems of the calculus of variations with generalized Lagrangian functionals that depend on a general linear operator K and defined on bounded-time intervals. Under assumptions of regularity, convexity and coercivity, we derive sufficient conditions ensuring the existence of a minimizer. Finally, we obtain necessary optimality conditions of Euler–Lagrange type. Main results are illustrated with special cases, when K is a general kernel operator and, in particular, with K the fractional integral of Riemann-Liouville and Hadamard. The application of our results to the recent fractional calculus of variations gives answer to an open question posed in doi:10.1155/2012/871912.
Origine : Fichiers produits par l'(les) auteur(s)