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Some global results for nonlinear eigenvalue problems. (English) Zbl 0212.16504


MSC:

47-02 Research exposition (monographs, survey articles) pertaining to operator theory
46B99 Normed linear spaces and Banach spaces; Banach lattices
47J05 Equations involving nonlinear operators (general)
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[1] Krasnoselski, M. A., Topological Methods in the Theory of Nonlinear Integral Equations (1965), Macmillan: Macmillan New York, Chap. 2
[2] Leray, J.; Schauder, J., Topologie et équations fonctionelles, Ann. Sci. École Norm., 51, 45-78 (1934), Suppl. 3 · JFM 60.0322.02
[5] (Keller, J. B.; Antman, S., Bifurcation Theory and Nonlinear Eigenvalue Problems (1969), Benjamin: Benjamin New York) · Zbl 0181.00105
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[9] Gantmacher, F. R.; Krein, M. G., Oszillationsmatrizen, Oszillationkerne und kleine Schwingungen mechanischer Systeme (1960), Academie-Verlag: Academie-Verlag Berlin · Zbl 0088.25103
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[15] Rabinowitz, P. H., Periodic solutions of nonlinear hyperbolic partial differential equations, Comm. Pure Appl. Math., 20, 145-205 (1967) · Zbl 0152.10003
[16] Nirenberg, L., On elliptic partial differential equations, Ann. Scuola, Norm. Super. Pisa Ser. 3, 13, 1-48 (1959)
[17] Bers, L.; John, F.; Schechter, M., Partial Differential Equations (1964), Interscience: Interscience New York, Chap. 4
[18] Moser, J., A rapidly convergent iteration method and nonlinear partial differential equations, Ann. Scuola, Norm. Super. Pisa Ser. 3, 20, 265-315 (1966) · Zbl 0144.18202
[19] Karlin, S., The existence of eigenvalues for integral operators, Trans. Amer. Math. Soc., 113, 1-17 (1964) · Zbl 0178.46804
[20] Parter, S. V., Nonlinear Eigenvalue Problems for Some Fourth-Order Equations: II. Fixed Point Methods, (Technical report #77 (Nov. 1969), Computer Sci. Dept., Univ. of Wisconsin), 1-46
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