The paper deals with ODEs with an advanced argument, in particular, with such equations as y (t) = (y(ÿt)) 1=ÿ , the simplest example is y (t) = y(2t). The corresponding initial-value problem with y(0) = y0 ¿ 0 has three types of solutions: (a) a unique analytic solution, (b) solutions of subexponen
Bounded solutions of nonlinear difference equations with advanced arguments
✍ Scribed by L. Díaz; R. Naulin
- Publisher
- Elsevier Science
- Year
- 2003
- Tongue
- English
- Weight
- 651 KB
- Volume
- 45
- Category
- Article
- ISSN
- 0898-1221
No coin nor oath required. For personal study only.
✦ Synopsis
sufficient conditions of existence and uniqueness of a-bounded and bounded solutions to the difference equation with advanced arguments z
192, are given. It is proven that under certain conditions it is possible to find positive numbers R, CL, such that from every initial condition < satisfying I<1 < R, a unique bounded solution, belonging to the ball (21 5 CL, starts.
📜 SIMILAR VOLUMES
The tollowing difference equation with deviating arguments: ) is a sequence of nonnegative numbers, ~rj : N ---+ N and limk--++oo crj(k) = +oc (j = 1,..., m). In the paper, sufficient conditions are established for all proper solutions of the above equation to be oscillatory.