Asymptotic Formula for Oscillatory Solutions of Some Singular NonlinearDifferential Equation

Abstract

Singular differential equation $(p\left(t\right)u^{\prime }{)}^{\prime }=p\left(t\right)f\left(u\right)$ is investigated. Here $f$ is Lipschitz continuous on $ℝ$ and has at least two zeros 0 and . The function $p$ is continuous on $[0,\infty )$ and has a positive continuous derivative on $(0,\infty )$ and $p\left(0\right)=0$. An asymptotic formula for oscillatory solutions is derived.