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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)
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[1] Krasnoselski, M.A, Topological methods in the theory of nonlinear integral equations, (1965), 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] \scP. H. Rabinowitz, Nonlinear Sturm-Liouville problems for second order ordinary differential equations, Comm. Pure Appl. Math., to appear. · Zbl 0206.09706
[4] \scM. G. Crandall and P. H. Rabinowitz, Nonlinear Sturm-Liouville eigenvalue problems and topological degree, J. Math. Mech., to appear. · Zbl 0206.09705
[5] ()
[6] Whyburn, G.T, Topological analysis, (1958), Princeton Univ. Press Princeton, N. J, Chap. 1
[7] \scL. Bauer, E. L. Riess, and H. B. Keller, “Antisymmetric Buckling of Hollow Spheres and Hemispheres,” preprint.
[8] \scM. G. Crandall and P. H. Rabinowitz, Bifurcation at simple eigenvalues, J. Functional Analysis, to appear. · Zbl 0219.46015
[9] Gantmacher, F.R; Krein, M.G, Oszillationsmatrizen, oszillationkerne und kleine schwingungen mechanischer systeme, (1960), Academie-Verlag Berlin · Zbl 0088.25103
[10] \scR. Turner, Nonlinear eigenvalue problems with nonlocal operators, J. Math. Mech., to appear. · 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 New York/London, Chap. 6 · Zbl 0164.13002
[13] Courant, R; Hilbert, D, (), Chap. 4
[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 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, (), 1-46
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