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Ljusternik-Schnirelman theory and non-linear eigenvalue problems. (English) Zbl 0233.47049

47J05 Equations involving nonlinear operators (general)
58E15 Variational problems concerning extremal problems in several variables; Yang-Mills functionals
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[1] Amann, H.: Ein Existenz- und Eindeutigkeitssatz f?r die Hammersteinsche Gleichung in Banachr?umen. Math. Z.111, 175-190 (1969). · Zbl 0176.45604 · doi:10.1007/BF01113284
[2] Amann, H.: Hammersteinsche Gleichungen mit kompakten Kernen. Math. Ann.186, 334-340 (1970). · Zbl 0185.22202 · doi:10.1007/BF01350597
[3] Berger, M. S.: A Sturm-Liouville theorem for non-linear elliptic partial differential equations. Ann. Scuola Norm. Sup PisaXX, 543-582 (1966). Corrections, ibid.XXII, 351-354 (1968). · Zbl 0147.09503
[4] Browder, F. E.: Infinite dimensional manifolds and non-linear elliptic eigenvalue problems. Ann. Math.82, 459-477 (1965). · Zbl 0136.12002 · doi:10.2307/1970708
[5] Browder, F. E.: Non-linear eigenvalue problems and Galerkin approximations. Bull. Amer. Math. Soc.74, 651-656 (1968). · Zbl 0162.20302 · doi:10.1090/S0002-9904-1968-11979-2
[6] Browder, F. E.: Existence theorems for non-linear partial differential equations. Proceeding of Symposia in Pure MathematicsXVI, 1-60 (1970). · Zbl 0212.27704
[7] Browder, F. E.: Nonlinear eigenvalue problems and group invariance. In F. E. Browder, ed. Functional Analysis and Related Fields, Springer 1970, 1-58. · Zbl 0213.41304
[8] Browder, F. E., Gupta, C. P.: Monotone operators and non-linear integral equations of Hammerstein type. Bull. Amer. Math. Soc.75, 1347-1353 (1969). · Zbl 0193.11204 · doi:10.1090/S0002-9904-1969-12420-1
[9] Coffman, C. V.: A minimum-maximum principle for a class of non-linear integral equations. J. Anal. Math.XXII, 391-418 (1969). · Zbl 0179.15601 · doi:10.1007/BF02786802
[10] Coffman, C. V.: Spectral theory of monotone Hammerstein operators. Pacific J. Math.36, 303-322 (1971). · Zbl 0212.46803
[11] Coffman, C. V.: Normalized iterations and non-linear eigenvalue problems of variational type (to appear).
[12] Kato, T.: Non-linear semigroups and evolution equations. J. Math. Soc. Japan.13, 508-520 (1967). · Zbl 0163.38303 · doi:10.2969/jmsj/01940508
[13] Krasnosel’skii, M. A.: Topological methods in the theory of non-linear integral equations. Oxford: Pergamon Press 1964.
[14] Lusternik, L., Schnirelman, L.: M?thodes topologiques dans les problemes variationels. Actualit?s scientifiques et industrielles 188 (1934).
[15] Palais, R. S.: Lusternik-Schnirelman theory on Banach manifolds. Topology5, 115-132 (1966). · Zbl 0143.35203 · doi:10.1016/0040-9383(66)90013-9
[16] Schwartz, J. T.: Generalizing the Lusternik-Schnirelman theory of critical points. Comm. Pure Appl. Math.17, 307-315 (1964). · Zbl 0152.40801 · doi:10.1002/cpa.3160170304
[17] Schwartz, J. T.: Non-linear functional analysis. New York: Gordon and Breach 1969. · Zbl 0203.14501
[18] Vainberg, M. M.: Variational methods for the study of non-linear operators. San Francisco: Holden-Day 1964.
[19] Weiss, S.: Nonlinear eigenvalue problems (to appear). · Zbl 0533.34018
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