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July/August 2014 Existence of minimizers for generalized Lagrangian functionals and a necessary optimality condition – Application to fractional variational problems
Loïc Bourdin, Tatiana Odzijewicz, Delfim F.M. Torres
Differential Integral Equations 27(7/8): 743-766 (July/August 2014).

Abstract

We study dynamic minimization problems of the calculus of variations with generalized Lagrangian functionals that depend on a general linear operator $K$ and are 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. The main results are illustrated with special cases, when $K$ is a general kernel operator and, in particular, with $K$ being 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 [Abstr. Appl. Anal. 2012, Art. ID 871912; doi:10.1155/2012/871912].

Citation

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Loïc Bourdin. Tatiana Odzijewicz. Delfim F.M. Torres. "Existence of minimizers for generalized Lagrangian functionals and a necessary optimality condition – Application to fractional variational problems." Differential Integral Equations 27 (7/8) 743 - 766, July/August 2014.

Information

Published: July/August 2014
First available in Project Euclid: 6 May 2014

zbMATH: 1340.26012
MathSciNet: MR3200762

Subjects:
Primary: 26A33, 49J05

Rights: Copyright © 2014 Khayyam Publishing, Inc.

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Vol.27 • No. 7/8 • July/August 2014
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