Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-23T13:53:22.886Z Has data issue: false hasContentIssue false
  • English
  • Français

An Oscillation Result for Singular Neutral Equations

Published online by Cambridge University Press:  20 November 2018

István Gyori  and
Janos Turi
István Gyori
Affiliation:
Department of Mathematics and Computing University of Veszprém 8201 Veszprém, Egyetem út 10 Pf 158 Hungary
Janos Turi
Affiliation:
Programs in Mathematical Sciences University of Texas at Dallas Richardson, Texas 75083 U.S.A.
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.

In this paper, extending the results in [ 1 ], we establish a necessary and sufficient condition for oscillation in a large class of singular (i.e., the difference operator is nonatomic) neutral equations.

Keywords

34K4034A37
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 37 , Issue 1 , 01 March 1994 , pp. 54 - 65
Copyright
Copyright © Canadian Mathematical Society 1994

References

1. Arino, O. and Göri, I., Necessary and sufficient condition for oscillation of a neutral Differential System with several delays, J. Differential Equations 81(1989), 98–105.Google Scholar
2. Bainov, D. D., Myshkis, A. D. and Zahariev, A. I., Necessary and sufficient conditions for oscillation of the solution of linear functional differential equations of neutral type with distributed delay, J. Math. Anal. Appl. 148(1990), 263–273.Google Scholar
3. Boas, R. P., Entire Functions, Academic Press, New York, 1954.Google Scholar
4. Burns, J. A., Cliff, E. M. and Herdman, T. L., A state-space model for an aeroelastic system.In: Proceedings, 22nd IEEE CDC, San Antonio, Texas, 1983, 1074–1077.Google Scholar
5. Burns, J. A., Herdman, T. L. and Stech, H. W., Linear functional differential equations as semigroups on product spaces, SIAM J. Math. Analysis 14(1983), 98–116.Google Scholar
6. Burns, J. A., Herdman, T. L. and Turi, J., Neutral functional integro-differential equations with weakly singular kernels, J. Math. Analysis Appl. 145(1990), 371–401.Google Scholar
7. Burns, J. A. and Ito, K., On well-posedness of'integro-differential equations in weighted L2 -spaces, CAMS Reports (91-11), University of Southern California, Los Angeles, California, April 1991.Google Scholar
8. Györi, I. and Ladas, G., Oscillation Theory of Delay Differential Equations with Applications, Oxford Science Publ., Clarendon Press, Oxford, 1991.Google Scholar
9. Hale, J. K., Theory of Functional Differential Equations, Springer-Verlag, New York, 1977.Google Scholar
10. Herdman, T. L. and Turi, J., Singular neutral equations. In: Distributed Parameter Control Systems: New Trends and Applications, (eds. G. Chen, Lee, E. B., L. Markus and W. Littman), Marcel-Dekker, (1990), 501–511.Google Scholar
11. Ito, K., On well-posedness of’ integro-differential equations with weakly singular kernels, CAMS Reports (91-9), University of Southern California, Los Angeles, California, April 1991.Google Scholar
12. Ito, K. andKappel, F., On integro-differential equations with weakly singular kernels. In: Differential Equations with Applications, (eds. Goldstein, J., Kappel, F. and W. Schappacher), Marcel Dekker, New York, 1991, 209–218.Google Scholar
13. Ito, K. and Turi, J., Numerical methods for a class of singular integro-differential equations based on semigroup approximation, SIAM J. Numerical Analysis 28(1991), 1698–1722.Google Scholar
14. Kappel, F and Zhang, Kangpei, On neutral functional differential equations with nonatomic difference operator, J. Math. Analysis and Appl. 113(1986), 311–343.Google Scholar
15. Özbay, H. and Turi, J., On input/output stabilization of singular integro-differential systems, preprint.Google Scholar
16. Pazy, A., Semigroup of Linear Operators and Applications to Partial Differential Equations, Springer- Verlag, New York, 1983.Google Scholar
17. Philos, Ch. G. and Sficas, Y. G., On the oscillation of neutral differential equations, J. Math. Anal. Appl. 170(1992), 299–321.Google Scholar
18. Widder, D. V., The Laplace Transform, Princeton Univ. Press, Princeton, New Jersey, 1946.Google Scholar