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References
M. S. Berger, Nonlinearity and Functional Analysis, Academic Press, N.Y., 1977.
Yu. G. Borisovich, V. G. Zvyagin and Yu. I. Sapronov, Nonlinear Fredholm mappings and Leary — Schauder Theory, Uspechi Mat. Nauk 32 (1977), 3–74.
L. Cesari, Functional analysis, nonlinear differential equations and the alternative method, Lecture Notes in Pure and Appl. Math., vol. 19, M. Dekker, N.Y. 1976, 1–197 (Editors: Cesari, Kannan, Shuur).
S. Fucik, Solvability of Nonlinear Equations and Boundary Value Problems, D. Reidel Publ. Comp., 1980.
G. E. Gaines and J. Mawhin, Coincidence degree for nonlinear differential equations, Lecture Notes in Math., vol. 568, Sprinver-Verlag, 1977.
A. Granas, The theory of compact vector fields and some of its applications to topology of functional spaces I, Rozprawy Math. 20 (1962), 1–93.
S. Kaniel, Quasicompact nonlinear operators in Banach spaces and applications, Arch. Rational Mech. Anal. 20 (1965), 259–278.
J. Mawhin, Stable homotopy and ordinary differential equations with nonlinear boundary conditions, Rocky Mountain J. Of Math., 7(3)-(1977), 417–424.
J. Mawhin, Topological Degree Methods in Nonlinear Boundary Value Problems, Regional Conf. Series in Math., Vol. 40, AMS, 1979.
P. S. Milojević, A generalization of Leray-Schauder theorem and surjectivity results for multivalued A-proper and pseudo mappings J. Nonlinear Anal., TMA, 1(3) (1977), 263–276.
P. S. Milojević, Fixed point theorems for multivalued approximable mappings, Proc. Amer. Math. Soc. 73(1) (1979), 65–72.
P. S. Milojević, The solvability of operator equations with asymptotic quasibounded nonlinearities, Proc. Amer. Math. Soc. 76(2) (1979)-293–298.
P. S. Milojević, Fredholm alternatives and surjectivity results for multivalued A-proper and condensing mappings with applications to nonlinear integral and differential equations, Czechoslovak Math. J. 30(105) (1980), 387–417.
P. S. Milojević, Approximation-solvability of some nonlinear operator equations with applications, Proc. Intern. Symp. Funct. Diff. Equat. and Bifurcation, July 1979, São Carlos, Brasil, Lecture Notes in Math. Vol. 799, Springer-Verlag, 289–316 (Ed. A. F. Ize).
P. S. Milojević, Approximation-solvability results for equations involving nonlinear perturbations of Fredholm mappings with applications to differential equations, in Functional Analysis, Holomorphy and Approx. Theory, Proc. Int. Sem., Rio de Janeiro, August, 1979, Lecture Notes in Pure and Applied Math., M. Dekker, N.Y. (Ed. G. Zapata, to appear).
P. S. Milojević, Continuation theory for A-proper and strongly A-closed mappings and their uniform limits and nonlinear perturbations of Fredholm mappings, in Functional Analysis, Holomorphy and Approx. Theory, Proc. Int. Sem., Rio de Janeiro, August 1980, North Holand Publ. Comp. (Ed. J. A. Barroso, to appear).
P. S. Milojević, Theory of A-proper and Pseudo A-closed Mappings, Habilitation Memoir, Univ. Federal de Minas Gerais, Belo Horizonte, Brasil, December 1980, 1–208.
L. Nirenberg, An application of generalized degree to a class of nonlinear problems, Troisième Colloque CBBRM d’analyse fonctionnelle, Vander, Louvain, 1971, 57–74.
L. Nirenberg, Topics in Nonlinear Functional Analysis, New York University Lecture Notes, 1973/74.
W. V. Petryshyn, On the approximation-solvability of equations involving A-proper and pseudo A-proper mappings, Bull. Amer. Soc. 81 (1975), 223–312.
S. I. Pohozaev, The solvability of nonlinear equations with odd operators, Funct. Anal. i Priloźen. 1 (1967), 66–73.
P. H. Rabinowitz, A note on a nonlinear elliptic equation, Indiana Univ. Math. J., 22(1)-(1972), 43–49.
I. V. Skrypnik, On the coercivity inequality for pairs of linear elliptic operators, Soviet Math. Doklady, 19(2) (1978), 324–327.
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Milojević, P.S. (1982). Solvability of operator equations involving nonlinear perturbations of Fredholm mappings of nonnegative index and applications. In: Guedes de Figueiredo, D., Hönig, C.S. (eds) Differential Equations. Lecture Notes in Mathematics, vol 957. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0066240
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DOI: https://doi.org/10.1007/BFb0066240
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