Previous |  Up |  Next

Article

Title: Monotone iterative technique and connectedness of the set of solutions (English)
Author: Rudolf, Boris
Language: English
Journal: Mathematica Bohemica
ISSN: 0862-7959
Volume: 125
Issue: 3
Year: 2000
Pages: 323-329
Summary lang: English
.
Category: math
.
Summary: The paper deals with the properties of a monotone operator defined on a subset of an ordered Banach space. The structure of the set of fixed points between the minimal and maximal ones is described. (English)
Keyword: order preserving operator
Keyword: ordered Banach space
Keyword: structure of the set of fixed points
Keyword: fixed points between the minimal and maximal ones
Keyword: connectedness of the set of solutions
MSC: 34C25
MSC: 46B40
MSC: 47H07
MSC: 47H10
idZBL: Zbl 0971.47033
idMR: MR1790123
.
Date available: 2009-09-24T21:43:53Z
Last updated: 2015-09-15
Stable URL: http://hdl.handle.net/10338.dmlcz/126133
.
Reference: [1] Amman H.: Fixed points equations and nonlinear eigenvalue problems in ordered Banach spaces.SIAM Rev. 18 (1976), 620-709. MR 0415432, 10.1137/1018114
Reference: [2] Deimling K.: Nonlinear Functional Analysis.Springer-Verlag, Berlin, 1985. Zbl 0559.47040, MR 0787404
Reference: [3] Fang Shuhong: Semilattice structure of fixed points set for increasing operators.Nonlinear Anal. 27 (1996), 793-796. MR 1402165, 10.1016/0362-546X(95)00075-7
Reference: [4] Gera M., Nieto J. J., Šeda V.: Periodic boundary value problems for nonlinear higher order ordinary differential equatíons.Appl. Math. Comput. 48 (1992), 71-82. MR 1147728, 10.1016/0096-3003(92)90019-W
Reference: [5] Hess P.: Periodic-Parabolic Boundary Value Problems and Positivity.Pitman Research Works in Math. Ser., Longman, 1991. Zbl 0731.35050, MR 1100011
Reference: [6] Krasnoseľskij M. A., Lusnikov A. V.: Fixed points with special properties.Dokl. Akad. Nauk 345 (1995), 303-305. (In Russian.) MR 1372832
Reference: [7] Ladde G. S., Lakshmikantham V., Vatsala A. S.: Monotone Iterative Techniques for Nonlinear Differential Equations.Pitman, Boston, 1986. MR 0855240
Reference: [8] Lakshmikantham V., Leela S.: Remarks on first and second order periodic boundary value problems.Nonlinear Anal. 8 (1984), 281-287. Zbl 0532.34029, MR 0738013, 10.1016/0362-546X(84)90050-6
Reference: [9] Rudolf B., Kubáček Z.: Remarks on J. J. Nieto's paper: Nonlinear second order periodic boundary value problems.J. Math. Anal. Appl. 146 (1990), 203-206. Zbl 0713.34015, MR 1041210, 10.1016/0022-247X(90)90341-C
Reference: [10] Šeda V.: Generalized boundary value problems and Fredholm mappings.Nonlinear Anal. 30 (1997), 1607-1616. MR 1490083, 10.1016/S0362-546X(97)00033-3
.

Files

Files Size Format View
MathBohem_125-2000-3_5.pdf 1.526Mb application/pdf View/Open
Back to standard record
Partner of
EuDML logo