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Some nonoscillation criteria for inclusions

Part of: General theory in ordinary differential equations

Published online by Cambridge University Press:  09 April 2009

Ravi P. Agarwal ,
Said R. Grace  and
Donal O'Regan
Ravi P. Agarwal
Affiliation:
Department of Mathematical Sciences, Florida Institute of Technology, Melbourne FL 32901, USA, agarwal@fit.edu
Said R. Grace
Affiliation:
Department of Engineering Mathematics, Cairo University Orman, Giza 12221, Egypt
Donal O'Regan
Affiliation:
Department of Mathematics, National University of Ireland, Galway, Ireland
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Abstract

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New nonoscillatory criteria are presented for second order differential inclusions. The theory relies on Ky Fan's fixed point theorem for upper semicontinuous multifunctions.

MSC classification

Secondary: 34A60: Differential inclusions
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 80 , Issue 1 , February 2006 , pp. 1 - 12
Copyright
Copyright © Australian Mathematical Society 2006

References

[1]Agarwal, R. P., Grace, S. R. and O'Regan, D., ‘On nonoscillatory solutions of differential inclusions’, Proc. Amer. Math. Soc. 131 (2003), 129–140.CrossRefGoogle Scholar
[2]Agarwal, R. P., Meehan, M., and O'Regan, D., Fixed point theory and applications (Cambridge University Press, Cambridge, 2001).CrossRefGoogle Scholar
[3]Agarwal, R. P. and O'Regan, D., ‘Nonlinear operator inclusions on the half line’, Math. Comput. Modelling 32 (2000), 1287–1296.CrossRefGoogle Scholar
[4]Cecchi, M., Marini, M., and Zecca, P., ‘Existence of bounded solutions for multivalued differential systems’, Nonlinear Anal. 9 (1985), 775–786.Google Scholar
[5]Dunford, N. and Schwartz, J., Linear operators I. General theory (Interscience, New York, 1958).Google Scholar
[6]Erbe, L. H., Kong, Q. K. and Zhang, B. G., Oscillation theory for functional differential equations (Marcel Dekker, New York, 1995).Google Scholar
[7]Jingfa, W., ‘On second order quasilinear oscillations’, Funkcial. Ekvac. 41 (1998), 25–54.Google Scholar
[8]Kusano, T., Ogata, A. and Usami, H., ‘Oscillation theory for a class of second order quasilinear ordinary differential equations with applications to partial differential equations’, Japan J. Math. 19 (1993), 131–147.CrossRefGoogle Scholar
[9]Ladde, G. S., Lakshmikantham, V. and Zhang, B. G., Oscillation theory of differential equations with deviating arguments (Marcel Dekker, New York, 1987).Google Scholar
[10]Singh, B., ‘Asymptotic nature of nonoscillatory solutions of nth order retarded differential equations’, SIAM J. Math. Anal. 6 (1975), 784–795.Google Scholar