On a classical problem of the calculus of variations without convexity assumptions
Annales de l'I.H.P. Analyse non linéaire, Volume 7 (1990) no. 2, p. 97-106
@article{AIHPC_1990__7_2_97_0,
     author = {Cellina, Arrigo and Colombo, Giovanni},
     title = {On a classical problem of the calculus of variations without convexity assumptions},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     publisher = {Gauthier-Villars},
     volume = {7},
     number = {2},
     year = {1990},
     pages = {97-106},
     zbl = {0702.49002},
     mrnumber = {1051230},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_1990__7_2_97_0}
}
Cellina, A.; Colombo, G. On a classical problem of the calculus of variations without convexity assumptions. Annales de l'I.H.P. Analyse non linéaire, Volume 7 (1990) no. 2, pp. 97-106. http://www.numdam.org/item/AIHPC_1990__7_2_97_0/

[A-T1] G. Aubert and R. Tahraoui, Théorèmes d'existence pour des problèmes du calcul des variations du type : Inf ∫L0 f (x, u' (x)) dx et Inf ∫L0 f (x, u (x), u' (x)) dx, J. Diff. Eq., Vol. 33, 1979, pp. 1-15. | MR 540812 | Zbl 0404.49001

[A-T2] G. Aubert and R. Tahraoui, Théorèmes d'existence en optimisation non convexe, Appl. Anal., Vol. 18, 1984, pp. 75-100. | MR 762866 | Zbl 0522.49002

[C-V] C. Castaing and M. Valadier, Convex analysis and measurable multifunctions, Lecture Notes in Math., Springer-Verlag, Berlin, 1977. | MR 467310 | Zbl 0346.46038

[Ce1] L. Cesari, An existence theorem without convexity conditions, S.I.A.M. J. Control, Vol. 12, 1974, pp. 319-331. | MR 383179 | Zbl 0255.49008

[Ce2] L. Cesari, Optimization-Theory and Applications, Springer-Verlag, New York, 1983. | MR 688142 | Zbl 0506.49001

[C] F.H. Clarke, Optimization and Nonsmooth Analysis, Wiley, New York, 1983. | MR 709590 | Zbl 0582.49001

[E] I. Ekeland, Discontinuités de champs hamiltoniens et existence de solutions optimales en calcul des variations, Publications Mathématiques de l'I.H.E.S., Vol. 47, 1977, pp. 5-32. | Numdam | MR 493584 | Zbl 0447.49015

[E-T] I. Ekeland and R. Temam, Convex Analysis and Variational Problems, North-Holland, Amsterdam, 1976. | MR 463994 | Zbl 0322.90046

[M1] P. Marcellini, Alcune osservazioni sull'esistenza del minimo di integrali del calcolo delle variazioni senza ipotesi di convessità, Rend. di Matem., (2), Vol. 13, 1980, pp. 271-281. | Zbl 0454.49015

[M2] P. Marcellini, A Relation Between Existence of Minima for Non Convex Integrals and Uniqueness for Non Strictly Convex Integrals of the Calculus of Variations, Proc. of Congress on Mathematical Theories of Optimization, | Zbl 0505.49009

S. Margherita Ligure, J.P. Cecconi and T. Zolezzi Ed., Lecture Notes in Math., Vol. 979, Springer-Verlag, Berlin, 1983. | MR 713802 | Zbl 0499.00010

[M3] P. Marcellini, Some Remarks on Uniqueness in the Calculus of Variations, Nonlinear Partial Differential Equations and their Applications, Collège de France Seminar, Vol. IV, Pitman, Boston, 1984. | MR 716516 | Zbl 0521.49005

[O] C. Olech, Integrals of Set-Valued Functions and Linear Optimal Control Problems, Colloque sur la Théorie Mathématique du Contrôle Optimal, C.B.R.M., Vander, Louvain, 1970, pp. 109-125. | Zbl 0261.49038

[R] J.P. Raymond, Conditions nécessaires et suffisantes d'existence de solutions en calcul des variations, Ann. Inst. H. Poincaré, Analyse non linéaire, Vol. 4, 1987, pp. 169-202. | Numdam | MR 886931 | Zbl 0641.49012