Oscillation and nonoscillation of the second order differential equation with delay depending on the unknown function in the case when β ds/r(s) < β holds are consider. The results obtained in this paper can be conjugated with the theorems given by Bainov et al. [
Asymptotic behaviour of the nonoscillatory solutions of differential equations of second order with delay depending on the unknown function
β Scribed by D.D. Bainov; N.T. Markova; P.S. Simeonov
- Publisher
- Elsevier Science
- Year
- 1998
- Tongue
- English
- Weight
- 357 KB
- Volume
- 91
- Category
- Article
- ISSN
- 0377-0427
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β¦ Synopsis
The asymptotic behaviour of the solutions of the differential equations
(r(t)x'(t))' + f(t,x(t),x(A(t,x(t)))) = 0
in the case when fog ds/r(s)= +oo is considered.
π SIMILAR VOLUMES
A superlinear first-order differential-functional equation is considered with a delay depending on the unknown function. Sufficient conditions are provided for the existence of positive solutions to the equation under consideration.
In this paper, we improve the Sturm comparison theorem and two nonoscillation criteria of LEIGHTON and WINTNER, and establish two variants of a WINTNER'S nonoscillatory criterion of the second order linear differential equation where r, c : [to,co) -+ IR, T > 0 a.e. on [to,m) and f , c E L 1 ( t o