Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-28T14:34:38.705Z Has data issue: false hasContentIssue false

Solvability of discontinuous functional differential systems in l(M)

Published online by Cambridge University Press:  17 February 2009

A. Cabada
Affiliation:
Departamento de Análise Matemática, Facultade de Matemáticas, Campus Sur, Universidade de Santiago de Compostela, 15782 Santiago de Compostela, Spain; e-mail: cabada@usc.es.
J. Ángel Cid
Affiliation:
Departamento de Matemáticas, E.U.P. de Linares, Universidad de Jaén C / Alfonso X el Sabio, no. 28, 23700, Linares, Jaén, Spain; e-mail: angelcid@ujaen.es.
S. Heikkilä
Affiliation:
Department of Mathematical Sciences, University of Oulu, Box 3000, FIN-90014, University of Oulu, Finland; e-mail: sheikki@cc.oulu.fi.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We study the existence of extremal solutions for an infinite system of first-order discontinuous functional differential equations in the Banach space of the bounded functions I(M).

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2006

References

[1]Biles, D. C. and Schechter, E., “Solvability of a finite or infinite system of discontinuous quasimonotone differential equations”, Proc. Amer. Math. Soc. 128 (2000) 33493360.CrossRefGoogle Scholar
[2]Cabada, A., Grossinho, M. R. and Minhós, F., “On the solvability of some discontinuous third order nonlinear differential equations with two point boundary conditions”, J. Math. Anal. Appl. 285 (2003) 174190.CrossRefGoogle Scholar
[3]Cabada, A. and Heikkilä, S., “Existence results for discontinuous functional differential systems”, submitted.Google Scholar
[4]Cabada, A. and Heikkilä, S., “Existence of solutions of third-order functional problems with nonlinear boundary conditions”, ANZIAM J. 46 (2004) 3344.CrossRefGoogle Scholar
[5]Carl, S. and Heikkilä, S., Nonlinear differential equations in ordered spaces (Chapman and Hall/CRC, Boca Raton, FI, USA, 2000).CrossRefGoogle Scholar
[6]Chaljub-Simon, A. and Volkmann, P., “Un théorème d'existence et de comparaison pour des équations différentielles dans les espaces de fonctions bornées”, C. R. Acad. Sci. Paris Sér. I Mart. 311 (1990) 515517.Google Scholar
[7]Cid, J. A., “On extending existence theory from scalar ordinary differential equations to infinite quasimonotone systems of functional equations”, Proc. Amer. Math. Soc. 133 (2005) 26612670.CrossRefGoogle Scholar
[8]Guillerme, J., “Intermediate value theorems and fixed point theorems for semi-continuous functions in product spaces”, Proc. Amer. Math. Soc. 123 (1995) 21192122.CrossRefGoogle Scholar
[9]Hu, S., “Fixed points for discontinuous quasi-monotone maps in n”, Proc. Amer. Math. Soc. 104 (1988) 11111114.Google Scholar
[10]Liz, E. and Pouso, R. L., “Existence theory for first order discontinuous functional differential equations”, Proc. Amer. Math. Soc. 130 (2002) 33013311.CrossRefGoogle Scholar
[11]Schmidt, S., “Fixed points for discontinuous quasi-monotone maps in sequence spaces”, Proc. Amer. Math. Soc. 115 (1992) 361363.Google Scholar
[12]Tarski, A., “A lattice-theoretical fixed point theorem and its applications”, Pacific J. Math. 5 (1955) 285309.CrossRefGoogle Scholar