A general mountain pass principle for locating and classifying critical points

N. Ghoussoub; D. Preiss

Annales de l'I.H.P. Analyse non linéaire (1989)

  • Volume: 6, Issue: 5, page 321-330
  • ISSN: 0294-1449

How to cite


Ghoussoub, N., and Preiss, D.. "A general mountain pass principle for locating and classifying critical points." Annales de l'I.H.P. Analyse non linéaire 6.5 (1989): 321-330. <http://eudml.org/doc/78181>.

author = {Ghoussoub, N., Preiss, D.},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {Ambrosetti-Rabinowitz theorem; saddle point; Mountain pass},
language = {eng},
number = {5},
pages = {321-330},
publisher = {Gauthier-Villars},
title = {A general mountain pass principle for locating and classifying critical points},
url = {http://eudml.org/doc/78181},
volume = {6},
year = {1989},

AU - Ghoussoub, N.
AU - Preiss, D.
TI - A general mountain pass principle for locating and classifying critical points
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1989
PB - Gauthier-Villars
VL - 6
IS - 5
SP - 321
EP - 330
LA - eng
KW - Ambrosetti-Rabinowitz theorem; saddle point; Mountain pass
UR - http://eudml.org/doc/78181
ER -


  1. [1] A. Ambrosetti and P.H. Rabinowitz, Dual Variational Methods in Critical Point Theory and Applications, J. Funct. Anal., Vol. 14, (1973), pp. 349-381. Zbl0273.49063MR370183
  2. [2] J.P. Aubin and I. Ekeland, Applied Non Linear Analysis, Pure and Applied Mathematics, Wiley Interscience Publication, 1984. Zbl0641.47066
  3. [3] H. Hofer, A Geometric Description of the Neighbourhood of a Critical Point Given by the Mountain Pass Theorem, J. London Math. Soc., 31, 1985, pp. 566-570. Zbl0573.58007MR812787
  4. [4] H. Hofer, A Strong Form of the Mountain Pass Theorem and Applications, Proceedings of a microprogram on Reaction diffusion Equations, Berkeley, 1986 (to appear). Zbl0678.58011MR843584
  5. [5] C. Kuratowski, Topology, Vol. II, Academic Press, New York and London, 1968. MR259835
  6. [6] L. Nirenberg, Variational and Topological Methods in Non-Linear Problems, Bull. Amer. Math. Soc., (N.S.), 4, 1981, pp. 267-302. Zbl0468.47040MR609039
  7. [7] P. Pucci and J. Serrin, A Mountain Pass Theorem, J. Diff. Eq., Vol. 60, 1985, pp. 142- 149. Zbl0585.58006MR808262
  8. [8] P. Pucci and J. Serrin, The Structure of the Critical Set in the Mountain Pass Theorem, Trans. A.M.S., Vol. 91, No. 1, 1987, pp. 115-132. Zbl0611.58019MR869402
  9. [9] P. Pucci and J. Serrin, Extensions of the Mountain Pass Theorem, J. Funct. Analysis, Vol. 59, 1984, pp. 185-210. Zbl0564.58012MR766489
  10. [10] P.H. Rabinowitz, Minimax Methods in Critical Point Theory with Applications to Differential Equations, C.B.M.S., A.M.S., No. 65, 1986. Zbl0609.58002MR845785
  11. [11] Qi Guijie, Extension of Moutain Pass Lemma, Kexue Tongbao, Vol. 32, No. 12, 1987. Zbl0655.58007MR914322
  12. [12] N. Ghoussoub, Location, Multiplicity and Morse Indices of Min-Max Critical Points (to appear), 1989. Zbl0736.58011MR1103905

Citations in EuDML Documents

  1. Guangcai Fang, The structure of the critical set in the general mountain pass principle
  2. Dimitrios A. Kandilakis, Athanasios N. Lyberopoulos, Multiplicity of positive solutions for some quasilinear Dirichlet problems on bounded domains in n
  3. G. Tarantello, On nonhomogeneous elliptic equations involving critical Sobolev exponent
  4. Patrizia Pucci, Vicenṭiu Rădulescu, The Impact of the Mountain Pass Theory in Nonlinear Analysis: a Mathematical Survey
  5. Begoña Barrios, Ida De Bonis, María Medina, Ireneo Peral, Semilinear problems for the fractional laplacian with a singular nonlinearity
  6. Jacques Giacomoni, Ian Schindler, Peter Takáč, Sobolev versus Hölder local minimizers and existence of multiple solutions for a singular quasilinear equation
  7. Fabrice Bethuel, Jean-Claude Saut, Travelling waves for the Gross-Pitaevskii equation I
  8. Dumitru Motreanu, A saddle point approach to nonlinear eigenvalue problems
  9. Pengfei Yuan, Shiqing Zhang, New Periodic Solutions for N-Body Problems with Weak Force Potentials
  10. Antonio Ambrosetti, Critical points and nonlinear variational problems

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