Nonoscillatory Solutions of Second-Order Superlinear Dynamic Equations with Integrable Coefficients

Abstract

The asymptotic behavior of nonoscillatory solutions of the superlinear dynamic equation on time scales ${\left(r\right(t\left)x^{\Delta }\right(t\left)\right)}^{\Delta }+p\left(t\right){\left|x\left(\sigma \right(t\left)\right)\right|}^{\gamma }\text{sgn}x\left(\sigma \right(t\left)\right)=0$, $\gamma >\mathrm{1,}$ is discussed under the condition that $P\left(t\right)={\text{lim}}_{\tau \to \infty }{\displaystyle {\int }_t^{\tau }p\left(s\right)\Delta s}$ exists and $P(t)\ge 0$ for large $t$.