×

zbMATH — the first resource for mathematics

Lusternik-Schnirelman category and nonlinear elliptic eigenvalue problems. (English) Zbl 0136.12003

PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Felix E. Browder, Nonlinear elliptic boundary value problems, Bull. Amer. Math. Soc. 69 (1963), 862 – 874. · Zbl 0127.31901
[2] Felix E. Browder, Nonlinear elliptic boundary value problems. II, Trans. Amer. Math. Soc. 117 (1965), 530 – 550. · Zbl 0127.31903
[3] Felix E. Browder, Variational methods for nonlinear elliptic eigenvalue problems, Bull. Amer. Math. Soc. 71 (1965), 176 – 183. · Zbl 0135.15802
[4] Felix E. Browder, Existence and uniqueness theorems for solutions of nonlinear boundary value problems, Proc. Sympos. Appl. Math., Vol. XVII, Amer. Math. Soc., Providence, R.I., 1965, pp. 24 – 49.
[5] F. E. Browder, Infinite dimensional manifolds and nonlinear elliptic eigenvalue problems, Ann. of Math, (to appear). · Zbl 0136.12002
[6] M. A. Krasnosel’skii, Topological methods in the theory of nonlinear integral equations, Translated by A. H. Armstrong; translation edited by J. Burlak. A Pergamon Press Book, The Macmillan Co., New York, 1964.
[7] Serge Lang, Introduction to differentiable manifolds, Interscience Publishers (a division of John Wiley & Sons, Inc.), New York-London, 1962. · Zbl 0103.15101
[8] L. A. Lusternik and L. G. Schnirelman, Topological methods in variational problems, Trudy Inst. Mat. Mech. Moscow State Univ. (1930), 1-68.
[9] J. Milnor, Morse theory, Based on lecture notes by M. Spivak and R. Wells. Annals of Mathematics Studies, No. 51, Princeton University Press, Princeton, N.J., 1963. · Zbl 0108.10401
[10] Marston Morse, The calculus of variations in the large, American Mathematical Society Colloquium Publications, vol. 18, American Mathematical Society, Providence, RI, 1996. Reprint of the 1932 original. · Zbl 0011.02802
[11] Richard S. Palais, Morse theory on Hilbert manifolds, Topology 2 (1963), 299 – 340. · Zbl 0122.10702 · doi:10.1016/0040-9383(63)90013-2 · doi.org
[12] R. S. Palais and S. Smale, A generalized Morse theory, Bull. Amer. Math. Soc. 70 (1964), 165 – 172. · Zbl 0119.09201
[13] Jacob T. Schwartz, Generalizing the Lusternik-Schnirelman theory of critical points, Comm. Pure Appl. Math. 17 (1964), 307 – 315. · Zbl 0152.40801 · doi:10.1002/cpa.3160170304 · doi.org
[14] S. Smale, Morse theory and a non-linear generalization of the Dirichlet problem, Ann. of Math. (2) 80 (1964), 382 – 396. · Zbl 0131.32305 · doi:10.2307/1970398 · doi.org
[15] M. M. Vainberg, Variational methods for the study of nonlinear operators, GITTL, Moscow, 1956.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.