Abstract
This paper is devoted to the applications of classical topological degrees to nonlinear problems involving various classes of operators acting between ordered Banach spaces. In this framework, the Leray-Schauder, Browder-Petryshyn, and Amann-Weiss degree theories are considered, and several existence results are obtained. The non-Archimedean case is also discussed.
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References
Brown, R. F.: A topological introduction to nonlinear analysis, Second edition, Birkhäuser Boston, Inc., Boston, MA, 2004
Deimling, K.: Nonlinear Functional Analysis, Springer-Verlag, Berlin-Heidelberg-New York, 1985
Drábek, P., Milota, J.: Lectures on nonlinear analysis, Plzen, Vydavatelský Servis, 2004
O’Regan, D., Cho, Y. J., Chen, Y. Q.: Topological degree theory and applications, Series in Mathematical Analysis and Applications, 10, Chapman & Hall/CRC, Boca Raton, FL, 2006
Takahashi, W.: Nonlinear functional analysis. Fixed point theory and its applications, Yokohama Publishers, Yokohama, 2000
Amann, H.: Fixed points of asymptotically linear maps in ordered Banach spaces. J. Funct. Anal., 14, 162–171 (1973)
Amann, H.: Fixed point equations and nonlinear eigenvalue problems in ordered Banach spaces. SIAM Review, 18, 620–709 (1976)
Amann, H.: Nonlinear operators in ordered Banach spaces and some applications to nonlinear boundary value problems, Nonlinear Operators and the Calculus of Variations, Bruxelles 1975, Lecture Notes in Math. #543, 1–55, Springer Verlag, Berlin, 1976
Petryshyn, W. V.: On nonlinear P-compact operators in Banach Space with applications to constructive fixed point theorems. J. Math. Anal. Appl., 15, 228–242 (1966)
Browder, F. E., Petryshyn, W. V.: The topological degree and Galerkin approximations for noncompact operators in Banach spaces. Bull. A.M.S., 74, 641–646 (1968)
Browder, F. E., Petryshyn, W. V.: Approximation methods and the generalized topological degree for nonlinear mappings in Banach spaces. J. Funct. Anal., 3, 217–245 (1969)
Petryshyn, W. V.: Approximation-Solvability of Nonlinear Functional and Differential Equations, Marcel Dekker Inc., New York-Basel-Hong Kong, 1993
Cristescu, R.: Ordered vector spaces and linear operators, Abacus Press, Kent, 1976
Amann, H., Weiss, S.: On the uniqueness of the topological degree. Math. Z., 130, 39–54 (1973)
Callegari, A. J., Nachman, A.: A nonlinear singular boundary value problem in the theory of pseudoplastic fluids. SIAM J. Appl. Math., 38, 275–281 (1980)
Kusano, T., Swanson, C. A.: Entire positive solutions of singular semilinear elliptic equations. Japan J. Math., 11(1), 145–155 (1985)
Edelson, A. L.: Entire solutions of singular elliptic equations. J. Math. Anal. Appl., 139, 523–532 (1989)
Deimling, K.: Fixed points of generalised P-compact operators. Math.Z., 115, 188–196 (1970)
Lloyd, N. G.: Degree Theory, Cambridge University Press, 1978
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Duma, A., Duma, I. The topological degree in ordered Banach spaces. Acta. Math. Sin.-English Ser. 24, 1583–1592 (2008). https://doi.org/10.1007/s10114-008-7509-1
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DOI: https://doi.org/10.1007/s10114-008-7509-1