Literature Cited
L. A. Lyusternik, “Topology of function spaces and the calculus of variations in the Large,” Tr. Mat. Inst. V. A. Steklova, Akad. Nauk SSSR, Leningr. Otdel.,19, (1947).
A. Ya. Zaslavskii, “Critical points of Lipschitz functions on smooth manifolds,” Sib. Mat. Zh.,22, No. 1, 87–93 (1981).
P. Clark, Optimization and Nonsmooth Analysis [Russian translation], Nauka, Moscow (1988).
A. V. Dmitruk, A. A. Milyutin, and N. P. Osmolovskii, “Lyusternik's theorem and the theory of extrema,” Usp. Mat. Nauk,35, No. 6, 11–46 (1980).
S. Lang, Introduction to the Theory of Differentiable Manifolds [Russian translation], Mir, Moscow (1967).
M. A. Krasnosel'skii, Topological Methods in the Theory of Nonlinear Integral Equations [in Russian], Gostekhizdat, Moscow (1956).
R. S. Palais, “Lusternik-Schnirelman theory on Banach manifolds,” Topology, No. 5, 115–132 (1966).
F. E. Browder, “Nonlinear eigenvalue problems and group invariance,” Funct. Anal. Rel. Fields, Berlin etc., 1–58 (1970).
A. Ambrosetti and P. H. Rabinowitz, “Dual variational methods in critical points and applications,” J. Funct. Anal.,14, 349–381 (1973).
R. T. Rockafellar, “Generalized directional derivatives and supgradients of nonconvex functions,” Can. J. Math.,32, 157–180 (1980).
K. C. Chang, “Variational methods for nondifferentiable functionals and their applications to partial differential equations,” J. Math. Anal. Appl.,80, 102–129 (1981).
L. Hörmander, “Sur la fonction d'appui des ensembles convexes dans une espace localement convexe,” Ark. Mat.,3, No. 2, 180–186 (1955).
Additional information
Yaroslavl'. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 33, No. 3, pp. 91–100, May–June, 1992.
Rights and permissions
About this article
Cite this article
Klimov, V.S. Minimax critical values of nonsmooth functionals. Sib Math J 33, 445–452 (1992). https://doi.org/10.1007/BF00970892
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00970892