Two-parametric conditionally oscillatory half-linear differential equations
Summary: We study perturbations of the nonoscillatory half-linear differential equation \[ (r(t)\Phi(x'))'+c(t)\Phi(x)=0, \] \(\Phi(x):=|x|^{p-2}x,\) \(p>1\). We find explicit formulas for the functions \(\widehat r\), \(\widehat c\) such that the equation \[ [(r(t)+\lambda\widehat r(t)) \Phi(x')]'+[c(t)+\mu\widehat c(t)] \Phi (x)=0 \] is conditionally oscillatory, that is, there exists a constant \(\gamma\) such that the previous equation is oscillatory if \(\mu-\lambda>\gamma\) and nonoscillatory if \(\mu-\lambda <\gamma\). The obtained results extend previous results concerning two-parametric perturbations of the half-linear Euler differential equation.
nonoscillatory half-linear differential equation
scientific article; zbMATH DE number 5888121