Existence of multiple fixed points for nonlinear operators and applications. (English) Zbl 1157.47039

This paper, using fixed point index theory, investigates multiplicity results for sublinear and asymptotically linear operators in ordered Banach spaces. Also, multiple solutions to a system of Hammerstein integral equations are studied as an application of the main multiplicity result.


47H10 Fixed-point theorems
47H07 Monotone and positive operators on ordered Banach spaces or other ordered topological vector spaces
45G15 Systems of nonlinear integral equations
Full Text: DOI


[1] Guo, D. J.: Nonlinear Functional Analysis, Shandong Science and Technology Press, Ji’nan, 1985 (in Chinese)
[2] Guo, D. J., Lakshmikantham, V.: Nonlinear Problem in Abstract Cones, Academic Press, Inc., Boston, 1988 · Zbl 0661.47045
[3] Guo, D. J.: The number of non-zero solutions to Hammerstein nonlinear integral equations and applications. Chinese Science Bulletin, 27, 257–260 (1982) (in Chinese)
[4] Amann, H.: Fixed point equations and nonlinear eigenvalue problems in ordered Banach spaces. SIAM Review, 18, 620–709 (1976) · Zbl 0345.47044
[5] Henderson, J., Thompson, H. B.: Existence of multiple solutions for second order boundary value problems. J. Diff. Equ., 166, 443–454 (2000) · Zbl 1013.34017
[6] Zhang, F. B.: A theorem of three solutions for periodic boundary value problems of second order differential equations. J. Sys. Sci. and Math. Scis., 20, 257–263 (2000) (in Chinese) · Zbl 0971.34006
[7] Liu, Z. L., Li, F. Y.: Multiple positive solutions of nonlinear two-point boundary value problems. J. Math. Anal. and Appl., 203, 610–625 (1996) · Zbl 0878.34016
[8] Shivaji, R.: A remark on the existence of three solutions via sub-super solutions. Lecture Notes in Pure and Applied Mathematics, 109, 561–566 (1987) · Zbl 0647.35031
[9] Sun, J. X., Zhang, K. M.: On the number for nonlinear operator equations and applications. J. Sys. Sci. and Complexity, 16, 229–235 (2003) · Zbl 1131.47308
[10] Zhang, K. M., Sun, J. X.: The multiple solution theorem for superlinear operator equations in Banach space and applications. Acta Mathematica Sinica, Chinese Series, 48, 99–108 (2005) · Zbl 1117.47304
[11] Deimling, K.: Nonlinear Functional Analysis, Springer-Verlag, New York, 1985 · Zbl 0559.47040
[12] Dugundji, J., Granas, A.: Fixed point theory, Monografie Matematyczne, PWN, Warsaw, 1982 · Zbl 0483.47038
[13] Krasnosel’skiĭ, M. A., Zabreĭko, P. P.: Geometrical Method of Nonlinear Analysis, Springer-Verlag, New York, 1984
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.