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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
[2] Deimling K.: Nonlinear Functional Analysis. Springer-Verlag, Berlin, 1985. MR 0787404 | Zbl 0559.47040
[3] Fang Shuhong: Semilattice structure of fixed points set for increasing operators. Nonlinear Anal. 27 (1996), 793-796. DOI 10.1016/0362-546X(95)00075-7 | MR 1402165
[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
[8] Lakshmikantham V., Leela S.: Remarks on first and second order periodic boundary value problems. Nonlinear Anal. 8 (1984), 281-287. DOI 10.1016/0362-546X(84)90050-6 | MR 0738013 | Zbl 0532.34029
[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. DOI 10.1016/0022-247X(90)90341-C | MR 1041210 | Zbl 0713.34015
[10] Šeda V.: Generalized boundary value problems and Fredholm mappings. Nonlinear Anal. 30 (1997), 1607-1616. DOI 10.1016/S0362-546X(97)00033-3 | MR 1490083
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