Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-27T09:13:00.523Z Has data issue: false hasContentIssue false
  • English
  • Français

Counterexamples to a Conjecture for Neutral Equations

Published online by Cambridge University Press:  20 November 2018

T. Krisztin ,
R. M. Mathsen  and
Xu Yuantong
T. Krisztin
Affiliation:
Bolyai Institute Aradi Vértanúk tere 1 H-6720 Szeged Hungary
R. M. Mathsen
Affiliation:
Mathematics Department North Dakota State University Fargo, North Dakota 58105-5075 U.S.A.
Xu Yuantong
Affiliation:
Mathematics Department Zhongshan University Guangzhou People's Republic of China 510275
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.

A collection of examples of first order linear neutral differential delay equations having a nonoscillatory solution with lim sup = ∞ and lim inf = 0 at ∞ is given. This disproves a recent conjecture about the asymptotic behavior of solutions to such equations.

Keywords

34K15
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 36 , Issue 1 , 01 March 1993 , pp. 74 - 77
Copyright
Copyright © Canadian Mathematical Society 1993

References

1. Anno, O. and Györi, I., Necessary and sufficient conditions for oscillation of a neutral differential system with several delays, J. Diff. Eqns. 81(1989), 98–105.Google Scholar
2. Farrell, K., Grove, E. A. and Ladas, G., Neutral delay differential equations with positive and negative coefficients, Appl Anal. 27(1988), 181–197.Google Scholar
3. Grammatikopoulos, M. K., Grove, E. A. and Ladas, G., Oscillation and asymptotic behavior of neutral differential equations with deviating arguments, Appl. Anal. 22(1986), 1–19.Google Scholar
4. Mathsen, R. M., Yuantong, Xu and Qiru, Wang, Asymptotics and oscillation for first order neutral functional differential equations, preprint.Google Scholar
5. Philos, Ch. G. and Sfleas, Y. G., On the nature of the nonoscillatory solutions of a class of neutral delay differential equations,]. Math. Anal. Appl. 154(1991),417–434.Google Scholar
6. Ruan, Shigui, Oscillations for first order neutral differential equations with variable coefficients, Bull. Austral. Math. Soc. 43(1991), 147–152. Google Scholar
7. Schultz, S. W., Necessary and sufficient conditions for oscillation of neutral equations with mixed arguments. In: Differential Equations and Applications, Proceedings of the Int. Conf. on the Theory and Appl. of Diff. Eqns., Columbus, Ohio, 1988, Ohio University Press, Athens, 1989.Google Scholar