Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations

Order

Volumn 22, Issue 3, 2005, Pages 223-239

  Nieto, Juan J ^a   Rodríguez López, Rosana ^a  

^a UNIVERSITY OF SANTIAGO DE COMPOSTELA   (Spain)

Author keywords

First order differential equation; Fixed point; Lower and upper solutions; Partially ordered set

Indexed keywords

EID: 33644688928     PISSN: 01678094     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11083-005-9018-5     Document Type: Article

References (7)

1. Amann, H.: Order Structures and Fixed Points. Mimeographed Lecture Notes, Ruhr-Universität, Bochum, 1977.
2. Cousot, P. and Cousot, R.: Constructive versions of Tarski's fixed point theorems, Pacific J. Math. 82 (1979), 43-57.
3. Heikkilä, S. and Lakshmikantham, V.: Monotone Iterative Techniques for Discontinuous Nonlinear Differential Equations, Marcel Dekker, Inc., New York, 1994.
4. Ladde, G.S., Lakshmikantham, V. and Vatsala, A.S.: Monotone Iterative Techniques for Nonlinear Differential Equations, Pitman, Boston, 1985.
5. Ran, A.C.M. and Reurings, M.C.B.: A fixed point theorem in partially ordered sets and some applications to matrix equations, Proc. Am. Math. Soc. 132 (2004), 1435-1443.
6. Tarski, A.: A lattice-theoretical fixpoint theorem and its applications, Pacific J. Math. 5 (1955), 285-309.
7. Zeidler, E.: Nonlinear Functional Analysis and Its Applications, Vol. 1: Fixed-Point Theorems, Springer, New York, 1986.