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


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)
Full Text: DOI


[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
[3] P. H. RabinowitzComm. Pure Appl. Math.; P. H. RabinowitzComm. Pure Appl. Math. · Zbl 0206.09706
[4] M. G. Crandall and P. H. RabinowitzJ. Math. Mech.; M. G. Crandall and P. H. RabinowitzJ. Math. Mech. · Zbl 0206.09705
[5] (Keller, J. B.; Antman, S., Bifurcation Theory and Nonlinear Eigenvalue Problems (1969), Benjamin: Benjamin New York) · Zbl 0181.00105
[6] Whyburn, G. T., Topological Analysis (1958), Princeton Univ. Press: Princeton Univ. Press Princeton, N. J, Chap. 1 · Zbl 0080.15903
[7] L. Bauer, E. L. Riess, and H. B. Keller; L. Bauer, E. L. Riess, and H. B. Keller
[8] M. G. Crandall and P. H. RabinowitzJ. Functional Analysis; M. G. Crandall and P. H. RabinowitzJ. Functional Analysis · Zbl 0219.46015
[9] Gantmacher, F. R.; Krein, M. G., Oszillationsmatrizen, Oszillationkerne und kleine Schwingungen mechanischer Systeme (1960), Academie-Verlag: Academie-Verlag Berlin · Zbl 0088.25103
[10] R. TurnerJ. Math. Mech.; R. TurnerJ. Math. Mech. · Zbl 0201.14501
[11] Krein, M. G.; Rutman, M. A., Linear operators which leave a cone in Banach space invariant, Amer. Math. Soc. Trans. Ser. 1, 10 (1950) · Zbl 0030.12902
[12] Ladyzhenskaya, O. A.; Uraltseva, N., Linear and Quasilinear Elliptic Equations (1968), Academic Press: Academic Press New York/London, Chap. 6 · Zbl 0164.13002
[13] Courant, R.; Hilbert, D., (Methods of Mathematical Physics, Vol. II (1962), Interscience: Interscience New York), Chap. 4 · Zbl 0099.29504
[14] Keller, H. B.; Cohen, D. S., Some positone problems suggested by nonlinear heat generation, J. Math. Mech., 16, 1361-1376 (1967) · Zbl 0152.10401
[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 · Zbl 0126.00207
[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
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.