Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-11-30T21:50:09.170Z Has data issue: false hasContentIssue false
  • English
  • Français

Strongly Monotone Solutions of Retarded Differential Equations

Published online by Cambridge University Press:  20 November 2018

Y. G. Sficas
Y. G. Sficas*
Affiliation:
Department of Mathematics, University of Ioannina, Ioannina, Greece
Rights & Permissions [Opens in a new window]

Extract

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.

Let us consider the retarded differential equation

1

for which the following assumptions are made:

(i) p: [t0, ∞) → [0, ∞) is continuous and not identically zero for all large t.

(ii) σ [t0, ∞)→ ℝ is continuous, strictly increasing,

(iii) φ: ℝ → ℝ is continuous, non-decreasing and

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 22 , Issue 4 , 01 December 1979 , pp. 403 - 412
Copyright
Copyright © Canadian Mathematical Society 1979

References

1. Kusano, T. and Onose, H., Oscillatory and asymptotic behaviour of sublinear retarded differential equations, Hiroshima Math. J. 4 (1974), 343-355.Google Scholar
2. Ladas, G., Ladde, G. and Papadakis, J. S., Oscillations of functional-differential equations generated by delays, J. Differential Equations 12 (1972), 385-395.Google Scholar
3. Ladas, G., Lakshmikantham, V. and Papadakis, J. S., Oscillations of higher-order retarded differential equations generated by the retarded argument, Symposium on delay and functional differential equations, University of Utah, March 7-11, 1972.Google Scholar
4. Ladas, G., Sharp conditions for oscillations caused by delays, University of Rhode Island, Technical Report No 64, September 1976.Google Scholar
5. Lovelady, D. L., Positive bounded solutions for a class of linear delay differential equations, Hiroshima Math. J. 6 (1976), 451-456.Google Scholar
6. Monk, J. D., Introduction to set theory, McGraw-Hill (1969).Google Scholar
7. Naito, M., Oscillations of differential inequalities with retarded argument, Hiroshima Math. J. 5 (1975), 187-192.Google Scholar
8. Sflcas, Y. and Staikos, V., The effect of retarded actions on nonlinear oscillations, Proc. Amer. Math. Soc. 46 (1974), 259-264.Google Scholar
9. Sficas, Y. and Staikos, V., Oscillations of differential equations with deviating arguments, Funkcial. Ekvac. 19 (1976), 35-43.Google Scholar
10. Shreve, W., Oscillation in first order nonlinear retarded argument differential equations, Proc. Amer. Math. Soc. 41 (1973), 565-568.Google Scholar
11. Staikos, V. and Stavroulakis, I., Bounded oscillations under the effect of retardations for differential equations of arbitrary order, Proc. Roy. Soc. Edinburgh Sect. A 77 (1977), 129-136.Google Scholar