We study solutions tending to nonzero constants for the third order differential equation with the damping term $${\left(a_1\left(t\right){\left(a_2\left(t\right)x^{\text{'}}\left(t\right)\right)}^{\text{'}}\right)}^{\text{'}}+q\left(t\right)x^{\text{'}}\left(t\right)+r\left(t\right)f\left(x\left(\varphi \left(t\right)\right)\right)=0$$ in the case when the corresponding second order differential equation is oscillatory.

We propose an approach for studying positivity of Green’s operators of a nonlocal boundary value problem for the system of $n$ linear functional differential equations with the boundary conditions $n_i{x}_i-{\sum }_{j=1}^n{m}_{ij}{x}_j={\beta }_i$, $i=1,\cdots ,n$, where $n_i$ and $m_{ij}$ are linear bounded “local” and “nonlocal“ functionals, respectively, from the space of absolutely continuous functions. For instance, $n_i{x}_i=x_i\left(\omega \right)$ or $n_i{x}_i=x_i\left(0\right)-x_i\left(\omega \right)$ and $m_{ij}{x}_j={\int }_0^{\omega }k\left(s\right)x_j\left(s\right)\mathrm{d}s+{\sum }_{r=1}^{n_{ij}}{c}_{ijr}{x}_j\left(t_{ijr}\right)$ can be considered. It is demonstrated that the positivity of Green’s operator of nonlocal problem follows from the positivity of Green’s operator...

We consider preservation of exponential stability for the scalar nonoscillatory linear equation with several delays $$\dot{x}\left(t\right)+\sum _{k=1}^m{a}_k\left(t\right)x\left(h_k\left(t\right)\right)=0,a_k\left(t\right)\ge 0$$ under the addition of new terms and a delay perturbation. We assume that the original equation has a positive fundamental function; our method is based on Bohl-Perron type theorems. Explicit stability conditions are obtained.

This paper is concerned with the traveling wave solutions and asymptotic spreading of delayed lattice differential equations without quasimonotonicity. The spreading speed is obtained by constructing auxiliary equations and using the theory of lattice differential equations without time delay. The minimal wave speed of invasion traveling wave solutions is established by investigating the existence and nonexistence of traveling wave solutions.

The equation to be considered is $$L_{n}y\left(t\right)+p\left(t\right)y\left(\tau \left(t\right)\right)=0.$$ The aim of this paper is to derive sufficient conditions for property (A) of this equation.