The article is concerned with the existence of positive solutions of the delay differential equations. The asymptotic properties of solutions are also treated.

This paper contains some sufficient conditions for the existence of positive solutions which are bounded below and above by positive functions for the first‐order nonlinear neutral differential equations. These equations can also support the existence of positive solutions approaching zero at infinity

Valveless pumping, also known as Liebau effect, can be described as the unidirectional flow of liquid in a system without valves that is caused by the asymmetry of placing of the periodically working pump. Recently, the research in this field has been reevoked, partially due to its possible application in nanotechnologies. In this paper, a configuration of one pipe and one tank is considered from the mathematical point of view. Qualitative properties of a class of nonlinear differential equations that model the assumed system configuration are investigated. New sufficient conditions for the existence of positive T-periodic solutions are given. Correspondingly, exponential stability of periodic solution is treated. Presented results are new. They extend and complement earlier ones in the literature.

The paper contains some suffcient conditions for the existence of positive solutions which are bounded below and above by positive functions for the nonlinear neutral differential equations of higher order. These equations can also support the existence of positive solutions approaching zero at infinity.

The paper deals with the existence of positive ω-periodic solutions for a class of nonlinear delay differential equations. For example, such equations represent the model for the survival of red blood cells in an animal. The sufficient conditions for the exponential stability of positive ω-periodic solution are also considered

We are concerned with the classical approach to atomic motions in the vicinity of a wire charged by an oscillating voltage. This mechanism has been proposed to serve for trapping cold neutral atoms. We prove that, under some conditions, the atom must either collide with the wire or escape to infinity in the radial direction. The presented results for the atom–wire problem extend and complement some earlier ones in the literature.