| Title:
|
Monotone iterative technique and connectedness of the set of solutions (English) |
| Author:
|
Rudolf, Boris |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| 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 |
| DOI:
|
10.21136/MB.2000.126133 |
| . |
| Date available:
|
2009-09-24T21:43:53Z |
| Last updated:
|
2020-07-29 |
| 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 |
| 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 |
| . |
