Existence of Multiple Fixed Points for Nonlinear Operators and Applications
Acta Mathematica Sinica, English Series
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Acta Mathematica Sinica, English Series  2008, Vol. 24 Issue (7): 1079-1088    DOI: 10.1007/s10114-007-5506-4
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Existence of Multiple Fixed Points for Nonlinear Operators and Applications
Jing Xian SUN1, Ke Mei SUN2
1. Department of Mathematics, Xuzhou Normal University, Xuzhou, 221116, P. R. China;
2. Department of Mathematics, Qufu Normal University, Qufu, 273165, P. R. China
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Abstract In this paper, by the fixed point index theory, the number of fixed points for sublinear and asymptotically linear operators via two coupled parallel sub-super solutions is studied. Under suitable conditions, the existence of at least nine or seven distinct fixed points for sublinear and asymptotically linear operators is proved. Finally, the theoretical results are applied to a nonlinear system of Hammerstein integral equations.
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Jing Xian SUN
Ke Mei SUN
Key wordscone   fixed point index   parallel sub-super solutions     
Received: 2005-09-30;
Fund: This work is supported by the National Natural Science Foundation of China (10671167, 10471075)
Cite this article:   
Jing Xian SUN,Ke Mei SUN. Existence of Multiple Fixed Points for Nonlinear Operators and Applications[J]. Acta Mathematica Sinica, English Series, 2008, 24(7): 1079-1088.
http://www.actamath.com/Jwk_sxxb_en//EN/10.1007/s10114-007-5506-4      or     http://www.actamath.com/Jwk_sxxb_en//EN/Y2008/V24/I7/1079
[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
[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)
[5] Henderson, J., Thompson, H. B.: Existence of multiple solutions for second order boundary value problems. J. Diff. Equ., 166, 443-454 (2000)
[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)
[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)
[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)
[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)
[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)
[11] Deimling, K.: Nonlinear Functional Analysis, Springer-Verlag, New York, 1985
[12] Dugundji, J., Granas, A.: Fixed point theory, Monografie Matematyczne, PWN, Warsaw, 1982
[13] Krasnosel'skil, M. A., Zabrelko, P. P.: Geometrical Method of Nonlinear Analysis, Springer-Verlag, New York, 1984
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