Asymptotic estimate for differential equation with power coefficients and power delays

Abstract

The paper analyzes the asymptotic bounds of solutions of
differential equation with power coefficients, power delays and a
forcing term in the form $ \dot y(t)=\sum\limits_{j=0}^{m}a_j
    t^{\alpha_j}y(t^{\lambda_j})+f(t)$, where $a_0$ is a negative
    real, $\lambda_0=1$ and $0<\lambda_i<1$, $i=1,\dots,m$. Some additional assumptions on power
    coefficients and a forcing term $f(t)$ are  considered to obtain an asymptotic
    estimate for solutions of the studied differential equation. The
    application of the result is illustrated by several examples.