Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-11-22T16:41:21.807Z Has data issue: false hasContentIssue false

Some nonoscillation criteria for inclusions

Published online by Cambridge University Press:  09 April 2009

Ravi P. Agarwal
Affiliation:
Department of Mathematical Sciences, Florida Institute of Technology, Melbourne FL 32901, USA, [email protected]
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
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.

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

Type
Research Article
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), 129140.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), 12871296.CrossRefGoogle Scholar
[4]Cecchi, M., Marini, M., and Zecca, P., ‘Existence of bounded solutions for multivalued differential systems’, Nonlinear Anal. 9 (1985), 775786.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), 2554.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), 131147.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), 784795.Google Scholar