An intermediate existence theory in the calculus of variations

Frank H. Clarke; Philip D. Loewen

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1989)

  • Volume: 16, Issue: 4, page 487-526
  • ISSN: 0391-173X

How to cite

top

Clarke, Frank H., and Loewen, Philip D.. "An intermediate existence theory in the calculus of variations." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 16.4 (1989): 487-526. <http://eudml.org/doc/84060>.

@article{Clarke1989,
author = {Clarke, Frank H., Loewen, Philip D.},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
language = {eng},
number = {4},
pages = {487-526},
publisher = {Scuola normale superiore},
title = {An intermediate existence theory in the calculus of variations},
url = {http://eudml.org/doc/84060},
volume = {16},
year = {1989},
}

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
PB - Scuola normale superiore
VL - 16
IS - 4
SP - 487
EP - 526
LA - eng
UR - http://eudml.org/doc/84060
ER -

References

top
  1. [1] L. Cesari, Optimization-Theory and Applications, Springer-Verlag, New York, 1983. Zbl0506.49001MR688142
  2. [2] F.H. Clarke, The Euler-Lagrange differential inclusion, J. Differential Equations19 (1975), 80-90. Zbl0323.49021MR388196
  3. [3] F.H. Clarke, Solutions périodiques des équations hamiltoniennes, Comptes Rendus Acad. Sci. Paris287 (1978), 951-952. Zbl0422.35005MR520777
  4. [4] F.H. Clarke, Optimization and Nonsmooth Analysis, Wiley Interscience, New York, 1983. Zbl0582.49001MR709590
  5. [5] F.H. Clarke, Hamiltonian trajectories and local minima of the dual action, Trans. Amer. Math. Soc.287 (1985), 239-251. Zbl0596.49030MR766217
  6. [6] F.H. Clarke - I. Ekeland, Nonlinear oscillations and boundary value problems for Hamiltonian systems, Arch. Rational Mech. Anal.78 (1982), 315-333. Zbl0514.34032MR653545
  7. [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. Zbl0559.49012MR756513
  8. [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. Zbl0563.49009MR779053
  9. [9] F.H. Clarke - R.B. Vinter, Existence and regularity in the small in the calculus of variations, J. Differential Equations59 (1985), 336-354. Zbl0727.49003MR807852
  10. [10] P.D. Loewen, On the Lavrentiev phenomenon, Canad. Math. Bull.30 (1987), 102-108. Zbl0579.49002MR879878
  11. [11] R.T. Rockafellar, Convex Analysis, Princeton Univ. Press, Princeton, N.J., 1970. Zbl0193.18401
  12. [12] R.T. Rockafellar, Existence theorems for general control problems of Bolza and Lagrange, Adv. in Math.15 (1975), 312-333. Zbl0319.49001MR365273
  13. [13] L. Tonelli, Sur une méthode directe du calcul des variations, Rend. Circ. Mat. Palermo39 (1915), 233-264; also in Opere Scelte (Vol. 2), 289-333, Cremonese, Rome, 1961. Zbl45.0615.02JFM45.0615.02
  14. [14] L. Tonelli, Fondamenti di Calcolo delle Variazioni (2 Vols.), Zanichelli, Bologna, 1921, 1923. JFM48.0581.09

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.