Increasing convergent and divergent solutions to nonlinear delayed differential equations. (English) Zbl 1449.34233

Diblík, Josef; Chupáč, Radoslav; Růžičková, Miroslava

Differ. Integral Equ. 32, No. 9-10, 493-516 (2019).

The paper deals with the following nonlinear delay differential system \[\dot{y}(t)=\sum_{k=1}^m\beta^k(t)[y(t-\delta_k)-y(t-\tau_k)]^{r_k}.\] It is obtained: criteria guaranteeing the existence of increasing and unbounded solutions, criteria guaranteeing the existence of increasing and convergent solutions, as well as inequalities comparing such solutions with some given increasing functions.

Reviewer: Leonid Berezanski (Beer-Sheva)

MSC:

34K12	Growth, boundedness, comparison of solutions to functional-differential equations
34K25	Asymptotic theory of functional-differential equations

Keywords:

nonlinear delay differential system; convergent and divergent solutions; instability