Fixed points of decreasing operators in ordered Banach spaces and applications to nonlinear second order elliptic equations. (English) Zbl 1191.47075

Summary: We consider some decreasing operators in ordered Banach spaces. We study the existence and uniqueness of fixed points and properties of the iterative sequences for these operators. Lastly, the results are applied to nonlinear second order elliptic equations.


47H10 Fixed-point theorems
47H07 Monotone and positive operators on ordered Banach spaces or other ordered topological vector spaces
47N20 Applications of operator theory to differential and integral equations
35J61 Semilinear elliptic equations
Full Text: DOI


[1] Guo, Dajun; Lakshmikantham, V., Nonlinear problems in abstract cones, (1988), Academic Press Boston · Zbl 0661.47045
[2] Guo, Dajun; Lakshmikantham, V.; Liu, Xinzhi, Nonlinear integral equations in abstract spaces, (1996), Kluwer Academic Publishers · Zbl 0866.45004
[3] Deimling, Klaus, Nonlinear functional analysis, (1985), Springer-Verlag Berlin, Heidelberg · Zbl 0559.47040
[4] Guo, Dajun, Positive fixed points and eigenvectors of noncompact decreasing operators with applications to nonlinear integral equations, Chin. ann. math. (ser. B), 4, 419-426, (1993) · Zbl 0805.47050
[5] Li, Fuyi, Zhandong liang, fixed-point theorems of \(\phi\)-concave (\(- \phi\)-convex) operator and application, J. systems sci. math. sci., 14, 4, 355-360, (1994), (in Chinese) · Zbl 0827.47046
[6] Zhang, Zhitao, Fixed point theorems for a class of noncompact decreasing operators and their applications, J. systems sci. math. sci., 18, 4, 422-426, (1998), (in Chinese) · Zbl 0933.47039
[7] Li, Fuyi; Feng, Jinfeng; Shen, Peilong, Fixed point theorems of some decreasing operators and applications, Acta math. sci., 42, 2, 193-196, (1999), (in Chinese) · Zbl 1027.47517
[8] Li, Ke; Liang, Jin; Xiao, Ti-Jun, A fixed point theorem for convex and decreasing operators, Nonlinear anal., 63, e209-e216, (2005) · Zbl 1159.47306
[9] Li, Ke; Liang, Jin; Xiao, Ti-Jun, Positive fixed points for nonlinear operators, Comput. math. appl., 50, 1569-1578, (2005) · Zbl 1080.47043
[10] Krasnosel’skii, M.A., Positive solutions of operator equations, (1964), Noordhoff Groningen, The Netherlands · Zbl 0121.10604
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.