Minimax principles for lower semicontinuous functions and applications to nonlinear boundary value problems

Andrzej Szulkin

Annales de l'I.H.P. Analyse non linéaire (1986)

  • Volume: 3, Issue: 2, page 77-109
  • ISSN: 0294-1449

How to cite

top

Szulkin, Andrzej. "Minimax principles for lower semicontinuous functions and applications to nonlinear boundary value problems." Annales de l'I.H.P. Analyse non linéaire 3.2 (1986): 77-109. <http://eudml.org/doc/78110>.

@article{Szulkin1986,
author = {Szulkin, Andrzej},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {minimax principles; Lusternik-Schnirelman theory; convex functions; critical points; Ekeland's variational principle},
language = {eng},
number = {2},
pages = {77-109},
publisher = {Gauthier-Villars},
title = {Minimax principles for lower semicontinuous functions and applications to nonlinear boundary value problems},
url = {http://eudml.org/doc/78110},
volume = {3},
year = {1986},
}

TY - JOUR
AU - Szulkin, Andrzej
TI - Minimax principles for lower semicontinuous functions and applications to nonlinear boundary value problems
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1986
PB - Gauthier-Villars
VL - 3
IS - 2
SP - 77
EP - 109
LA - eng
KW - minimax principles; Lusternik-Schnirelman theory; convex functions; critical points; Ekeland's variational principle
UR - http://eudml.org/doc/78110
ER -

References

top
  1. [1] A. Ambrosetti and P.H. Rabinowitz, Dual variational methods in critical point theory and applications. J. Func. Anal., t. 14, 1973, p. 349-381. Zbl0273.49063MR370183
  2. [2] J.P. Aubin and I. Ekeland, Applied Nonlinear Anahlsis. Wiley, New York, 1984. Zbl0641.47066MR749753
  3. [3] V. Barbu, Nonlinear Semigroups and Differential Equations in Banach Spaces. Editura Academiei. Bucarest and Nordhoff, Leyden, 1976. Zbl0328.47035MR390843
  4. [4] H. Brézis, Opérateurs Maximaux Monotones et Semi-groupes de Contractions dans les Espaces de Hilbert. North-Holland, Amsterdam, 1973. Zbl0252.47055MR348562
  5. [5] H. Brézis, Monotonicity methods in Hilbert spaces and some applications to nonlinear partial differential equations. In: Contributions to Nonlinear Functional Analysis. E. Zarantanello ed., Academic Press, New York, 1971, p. 101-156. Zbl0278.47033MR394323
  6. [6] H. Brézis, Some variational problems with lack of compactness, Proc. of the 1983 AMS Summer Institute on Nonl. Func. Anal. and Appl., Amer. Math. Soc. (to appear). Zbl0617.35041MR843559
  7. [7] H. Brézis and L. Nirenberg, Characterizations of the ranges of some nonlinear operators and applications to boundary value problems. Ann. Scuola Norm. Sup. Pisa, Ser. IV, t. 5, 1978, p. 225-326. Zbl0386.47035MR513090
  8. [8] K.C. Chang, Variational methods for non-differentiable functionals and their applications to partial differential equations. J. Math. Anal. Appl., t. 80, 1981, p. 102-129. Zbl0487.49027MR614246
  9. [9] D.C. Clark, A variant of the Ljusternik-Schnirelmann theory. Indiana Univ. Math. J., t. 22, 1972, p. 65-74. Zbl0228.58006MR296777
  10. [10] J.P. Dias, Variational inequalities and eigenvalue problems for nonlinear maximal monotone operators in a Hilbert space. Amer. J. Math., t. 97, 1975, p. 905-914. Zbl0319.47040MR420354
  11. [11] J.P. Dias and J. Hernández, A Sturm-Liouville theorem for some odd multivalued maps. Proc. Amer. Math. Soc., t. 53, 1975, p. 72-74. Zbl0285.47037MR377632
  12. [12] G. Duvaut and J.L. Lions, Inequalities in Mechanics and Physics. Springer, Berlin, 1976. Zbl0331.35002MR521262
  13. [13] I. Ekeland, Nonconvex minimization problems. Bull. Amer. Math. Soc., t. 1, 1979, p. 443-474. Zbl0441.49011MR526967
  14. [14] D. G. de FIGUEIREDO and S. Solimini, A variational approach to superlinear elliptic problems. Comm. P. D. E., t. 9, 1984, p. 699-717. Zbl0552.35030MR745022
  15. [15] L.I. Hedberg, Spectral synthesis and stability in Sobolev spaces. Springer Lecture Notes in Mathematics, t. 779, 1980, p. 73-103. Zbl0469.31003MR576040
  16. [16] S.T. Hu, Homotopy Theory, Academic Press, New York, 1959. Zbl0088.38803MR106454
  17. [17] D. Kinderlehrer and G. Stampacchia, An Introduction to Variational Inequalities and Their Applications. Academic Press, New York, 1980. Zbl0457.35001MR567696
  18. [18] K. Kuratowski, Topologie I, PWN, Warsaw, 1958. Zbl0078.14603
  19. [19] J. Mawhin and M. Willem, Multiple solutions of the periodic boundary value problem for some forced pendulum-type equations. J. Diff. Eq., t. 52, 1984, p. 264- 287. Zbl0557.34036MR741271
  20. [20] L. Nirenberg, Variational and topological methods in nonlinear problems. Bull. Amer. Math. Soc., t. 4, 1981, p. 267-302. Zbl0468.47040MR609039
  21. [21] P.H. Rabinowitz, Variational methods for nonlinear eigenvalue problems, Proc. Sym. on Eigenvalues of Nonlinear Problems. Edizioni Cremonese, Rome, 1974, p. 143-195. MR464299
  22. [22] P.H. Rabinowitz, Some minimax theorems and applications to nonlinear partial differential equations. In: Nonlinear Analysis, A collection of papers in honor of E. Rothe, L. Cesari, R. Kannan and H. F. Weinberger ed., Academic Press, New York, 1978, p. 161-177. Zbl0466.58015MR501092
  23. [23] P.H. Rabinowitz, Some critical point theorems and applications to semilinear elliptic partial differential equations. Ann. Scuola Norm. Sup. Pisa, Ser. IV, t. 5, 1978, p. 215-223. Zbl0375.35026MR488128
  24. [24] P.H. Rabinowitz, Some aspects of critical point theory, MRC Tech. Rep. # 2465, Madison, Wisconsin, 1983. 
  25. [25] J.T. Schwartz, Nonlinear Functional Analysis. Gordon and Breach, New York, 1969. Zbl0203.14501MR433481
  26. [26] M. Struwe, Multiple solutions of differential equations without the Palais-Smale condition. Math. Ann., t. 261, 1982, p. 399-412. Zbl0506.35034MR679798
  27. [27] M. Struwe, Generalized Palais-Smale conditions and applications. Vorlesungsreihe SFB # 17, Bonn, 1983. Zbl0534.58021
  28. [28] I. Ekeland and J.M. Lasry, On the number of periodic trajectories for a Hamiltonian flow on a convex energy surface. Ann. Math., t. 112, 1980, p. 283-319. Zbl0449.70014MR592293

Citations in EuDML Documents

top
  1. Pavol Quittner, On positive solutions of semilinear elliptic problems
  2. Nikolaos Halidias, Nikolaos S. Papageorgiou, Quasilinear elliptic problems with multivalued terms
  3. Jean Mawhin, Nonlinear boundary value problems involving the extrinsic mean curvature operator
  4. Nikolaos S. Papageorgiou, Nikolaos Yannakakis, Multiple solutions for nonlinear periodic problems with discontinuities
  5. Giovanni Mancini, Roberta Musina, Holes and obstacles
  6. Andrzej Szulkin, Ljusternik-Schnirelmann theory on C 1 -manifolds
  7. Yang Jianfu, Positive solutions of an obstacle problem
  8. Gianni Arioli, Filippo Gazzola, Weak solutions of quasilinear elliptic PDE's at resonance
  9. Dumitru Motreanu, A saddle point approach to nonlinear eigenvalue problems

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.