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On the number of solutions of nonlinear equations in ordered Banach spaces. (English) Zbl 0244.47046

MSC:
47H10 Fixed-point theorems
47H05 Monotone operators and generalizations
47B60 Linear operators on ordered spaces
47J05 Equations involving nonlinear operators (general)
45G10 Other nonlinear integral equations
46A40 Ordered topological linear spaces, vector lattices
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[1] Agmon, S.; Douglis, A.; Nirenberg, L., Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions, I, Comm. pure appl. math., XII, 623-727, (1959) · Zbl 0093.10401
[2] Amann, H., On the existence of positive solutions of nonlinear elliptic boundary value problems, Indiana univ. math. J., 21, 125-146, (1971) · Zbl 0219.35037
[3] \scH. Amann, Existence of multiple solutions for nonlinear elliptic boundary value problems, Indiana Univ. Math. J., to appear. · Zbl 0222.35023
[4] Badoev, A.L.; Sadovskii, B.N., An example of a densifying operator in the theory of differential equations with a deviating argument of neutral type, Soviet math. dokl., 10, 724-728, (1969) · Zbl 0196.11103
[5] Browder, F.E., Estimates and existence theorems for elliptic boundary value problems, (), 365-372 · Zbl 0093.29402
[6] Browder, F.E., A continuity property for adjoints of closed operators in Banach spaces, and its application to elliptic boundary value problems, Duke math. J., 28, 157-182, (1961) · Zbl 0102.31502
[7] Browder, F.E., Nonlinear operators and nonlinear equations of evolution in Banach spaces, (), to appear · Zbl 0176.45301
[8] Darbo, G., Punti uniti in transformazioni a codominio non compatto, (), 84-92 · Zbl 0064.35704
[9] Gel’fand, I.M., Some problems in the theory of quasilinear equations, Amer. math. soc. transl. ser. 2, 29, 295-381, (1963) · Zbl 0127.04901
[10] Hamilton, J.D., Noncompact mappings and cones in Banach spaces, () · Zbl 0246.47063
[11] Jameson, G., Ordered linear spaces, () · Zbl 0196.13401
[12] Jörgens, K., Lineare integraloperatoren, (1970), Teubner Stuttgart · Zbl 0207.44602
[13] Krasnosel’skii, M.A., Fixed points of cone-compressing or cone-extending operators, Soviet math. dokl., 1, 1285-1288, (1960) · Zbl 0098.30902
[14] Krasnosel’skii, M.A., Positive solutions of operator equations, (1964), Noordhoff Groningen · Zbl 0121.10604
[15] Krasnosel’skii, M.A.; Stecenko, V.Ja., Some nonlinear problems with many solutions, Amer. math. soc. transl., ser. 2, 54, 29-48, (1966)
[16] Krein, M.G.; Rutman, M.A., Linear operators leaving invariant a cone in a Banach space, Amer. math. soc. transl., ser. 1, 10, 1-128, (1962) · Zbl 0030.12902
[17] Ladyzhenskaya, O.A.; Ural’tseva, N.N., Linear and quasilinear elliptic equations, (1968), Academic Press New York · Zbl 0164.13002
[18] Laetsch, T.W., Existence and bounds for multiple solutions of nonlinear equations, SIAM J. appl. math., 18, 389-400, (1970) · Zbl 0193.05001
[19] \scT. W. Laetsch, Existence and bounds for multiple solutions of nonlinear equations, II, to appear. · Zbl 0193.05001
[20] Laetsch, T.W., On the number of solutions of boundary value problems with convex nonlinearities, J. math. anal. appl., 35, 389-404, (1971) · Zbl 0191.40102
[21] \scT. W. Laetsch, Uniqueness for sublinear boundary value problems, to appear. · Zbl 0247.35052
[22] Miranda, C., Partial differential equations of elliptic type, (1970), Springer Verlag New York · Zbl 0198.14101
[23] Nussbaum, R.D., The fixed point and fixed point theorems for k-set-contractions, () · Zbl 0174.45402
[24] Nussbaum, R.D., The fixed point index for local condensing maps, Ann. mat. pura appl., LXXXIX, 217-258, (1971) · Zbl 0226.47031
[25] Nussbaum, R.D., A generalization of the ascoli theorem and an application to functional differential equations, J. math. anal. appl., 35, 600-610, (1971) · Zbl 0215.19501
[26] Protter, M.H.; Weinberger, H.F., Maximum principles in differential equations, (1967), Prentice-Hall Englewood Cliffs, NJ · Zbl 0153.13602
[27] Rothe, E., Theorie der topologischen ordnung und der vektorfelder in banachschen Räumen, Comp. math., 5, 177-197, (1937) · Zbl 0018.13304
[28] \scD. H. Sattinger, Monotone methods in nonlinear elliptic and parabolic boundary value problems, to appear. · Zbl 0223.35038
[29] Schaefer, H.H., Topological vector spaces, (1971), Springer Verlag New York · Zbl 0217.16002
[30] Shampine, L.F., Some nonlinear eigenvalue problems, J. math. mech., 17, 1065-1072, (1968) · Zbl 0157.18602
[31] Courant, R.; Hilbert, D., ()
[32] Choquet-Bruhat, Y.; Leray, J., Sur le problème de Dirichlet, quasilinéaire, d’ordre 2, C. R. acad. sci. Paris, ser. A, 274, 81-85, (1972) · Zbl 0227.35045
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