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Minimal and maximal solutions to systems of differential equations with a singular matrix

Published online by Cambridge University Press:  17 February 2009

Tadeusz Jankowski
Tadeusz Jankowski
Affiliation:
Technical University of Gdańsk, Department of Differential Equations, 11/12 G. Narutowicz Str., 80–952 Gdańsk, Poland; e-mail: [email protected].
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Abstract

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The monotone iterative technique is applied to a system of ordinary differential equations with a singular matrix. The existence of extremal solutions is proved.

Type
Research Article
Information
The ANZIAM Journal , Volume 45 , Issue 2 , October 2003 , pp. 223 - 231
Copyright
Copyright © Australian Mathematical Society 2003

References

[1]Bellman, R., Methods of nonlinear analysis, Volume 2 (Academic Press, New York, 1973).Google Scholar
[2]Jankowski, T. and Lakshmikantham, V., “Monotone iterations for differential equations with a parameter”, J. Appl. Math. Stoch. Anal. 10 (1997) 273–278.CrossRefGoogle Scholar
[3]Ladde, G. S., Lakshmikantham, V. and Vatsala, A. S., Monotone iterative techniques for nonlinear differential equations (Pitman, Boston, 1985).Google Scholar
[4]Lakshrnikantham, V. and Vatsala, A. S., Generalized quasilinearization for nonlinear problems (Kluwer, Derdrecht, 1998).CrossRefGoogle Scholar
[5]Nieto, J. J., “Quadratic approximation of solutions for ordinary differential equations”, Bull. Austral. Math. Soc. 55 (1997) 161–168.CrossRefGoogle Scholar
[6]Nieto, J. J. and Alvarez-Noriega, N., “Periodic boundary value problems for nonlinear first-order ordinary differential equations”, Acta Math. Hungar. 71 (1996) 49–58.CrossRefGoogle Scholar
[7]Yin, Y., “Remarks on first-order differential equations with anti-periodic boundary conditions”, Nonlinear limes and Digest 2 (1995) 83–94.Google Scholar
[8]Yin, Y., “Monotone iterative technique and quasilinearization for some anti-periodic problems”, Nonlinear World 3 (1996) 253–266.Google Scholar