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

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.

MSC:

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