Article
Keywords:
order preserving operator; ordered Banach space; structure of the set of fixed points; fixed points between the minimal and maximal ones; connectedness of the set of solutions
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.
References:
[1] Amman H.:
Fixed points equations and nonlinear eigenvalue problems in ordered Banach spaces. SIAM Rev. 18 (1976), 620-709.
DOI 10.1137/1018114 |
MR 0415432
[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
[5] Hess P.:
Periodic-Parabolic Boundary Value Problems and Positivity. Pitman Research Works in Math. Ser., Longman, 1991.
MR 1100011 |
Zbl 0731.35050
[6] Krasnoseľskij M. A., Lusnikov A. V.:
Fixed points with special properties. Dokl. Akad. Nauk 345 (1995), 303-305. (In Russian.)
MR 1372832
[7] Ladde G. S., Lakshmikantham V., Vatsala A. S.:
Monotone Iterative Techniques for Nonlinear Differential Equations. Pitman, Boston, 1986.
MR 0855240