Differential and Integral Equations
- Differential Integral Equations
- Volume 27, Number 7/8 (2014), 743-766.
Existence of minimizers for generalized Lagrangian functionals and a necessary optimality condition – Application to fractional variational problems
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].
Differential Integral Equations, Volume 27, Number 7/8 (2014), 743-766.
First available in Project Euclid: 6 May 2014
Permanent link to this document
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Bourdin, Loïc; Odzijewicz, Tatiana; Torres, Delfim F.M. Existence of minimizers for generalized Lagrangian functionals and a necessary optimality condition – Application to fractional variational problems. Differential Integral Equations 27 (2014), no. 7/8, 743--766. https://projecteuclid.org/euclid.die/1399395751