An intermediate existence theory in the calculus of variations
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 16 (1989) no. 4, pp. 487-526. 
@article{ASNSP_1989_4_16_4_487_0,
     author = {Clarke, Frank H. and Loewen, Philip D.},
     title = {An intermediate existence theory in the calculus of variations},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {487--526},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 16},
     number = {4},
     year = {1989},
     mrnumber = {1052732},
     zbl = {0727.49004},
     language = {en},
     url = {http://archive.numdam.org/item/ASNSP_1989_4_16_4_487_0/}
}
TY  - JOUR
AU  - Clarke, Frank H.
AU  - Loewen, Philip D.
TI  - An intermediate existence theory in the calculus of variations
JO  - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY  - 1989
SP  - 487
EP  - 526
VL  - 16
IS  - 4
PB  - Scuola normale superiore
UR  - http://archive.numdam.org/item/ASNSP_1989_4_16_4_487_0/
LA  - en
ID  - ASNSP_1989_4_16_4_487_0
ER  - 
%0 Journal Article
%A Clarke, Frank H.
%A Loewen, Philip D.
%T An intermediate existence theory in the calculus of variations
%J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
%D 1989
%P 487-526
%V 16
%N 4
%I Scuola normale superiore
%U http://archive.numdam.org/item/ASNSP_1989_4_16_4_487_0/
%G en
%F ASNSP_1989_4_16_4_487_0
Clarke, Frank H.; Loewen, Philip D. An intermediate existence theory in the calculus of variations. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 16 (1989) no. 4, pp. 487-526. http://archive.numdam.org/item/ASNSP_1989_4_16_4_487_0/

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

[2] F.H. Clarke, The Euler-Lagrange differential inclusion, J. Differential Equations 19 (1975), 80-90. | MR | Zbl

[3] F.H. Clarke, Solutions périodiques des équations hamiltoniennes, Comptes Rendus Acad. Sci. Paris 287 (1978), 951-952. | MR | Zbl

[4] F.H. Clarke, Optimization and Nonsmooth Analysis, Wiley Interscience, New York, 1983. | MR | Zbl

[5] F.H. Clarke, Hamiltonian trajectories and local minima of the dual action, Trans. Amer. Math. Soc. 287 (1985), 239-251. | MR | Zbl

[6] F.H. Clarke - I. Ekeland, Nonlinear oscillations and boundary value problems for Hamiltonian systems, Arch. Rational Mech. Anal. 78 (1982), 315-333. | MR | Zbl

[7] F.H. Clarke - R.B. Vinter, On the conditions under which the Euler equation or the maximum principle hold, Appl. Math. Optim. 12 (1984), 73-79. | MR | Zbl

[8] F.H. Clarke - R.B. Vinter, Regularity properties of solutions to the basic problem in the calculus of variations, Trans. Amer. Math. Soc. 289 (1985), 73-98. | MR | Zbl

[9] F.H. Clarke - R.B. Vinter, Existence and regularity in the small in the calculus of variations, J. Differential Equations 59 (1985), 336-354. | MR | Zbl

[10] P.D. Loewen, On the Lavrentiev phenomenon, Canad. Math. Bull. 30 (1987), 102-108. | MR | Zbl

[11] R.T. Rockafellar, Convex Analysis, Princeton Univ. Press, Princeton, N.J., 1970. | Zbl

[12] R.T. Rockafellar, Existence theorems for general control problems of Bolza and Lagrange, Adv. in Math. 15 (1975), 312-333. | MR | Zbl

[13] L. Tonelli, Sur une méthode directe du calcul des variations, Rend. Circ. Mat. Palermo 39 (1915), 233-264; also in Opere Scelte (Vol. 2), 289-333, Cremonese, Rome, 1961. | JFM

[14] L. Tonelli, Fondamenti di Calcolo delle Variazioni (2 Vols.), Zanichelli, Bologna, 1921, 1923. | JFM