Increasing convergent and divergent solutions to nonlinear delayed differential equations

Abstract

The paper is concerned with a nonlinear system of delayed differential equations as a generalization of an equation describing a simple model of the fluctuation of biological populations. The dependence of the behavior of monotone solutions on the coefficients and delays is studied and optimal sufficient conditions are derived for the existence of increasing and unbounded solutions and for the existence of increasing and convergent solutions. Inequalities estimating such solutions with some given increasing functions are derived as well. The results are compared with the linear case illustrated by examples, and open problems are formulated.