Half-linear Euler differential equations in the critical case
Abstract
We investigate oscillatory properties of the perturbed
half-linear Euler differential equation
$$
\bigl(\Phi(x')\bigr)'+\frac{\gamma_p}{t^p}\Phi(x)=0,\quad
\Phi(x):=|x|^{p-2}x,\ \gamma_p:=\left(\frac{p-1}{p}\right)^p.
$$
A perturbation is also allowed in the coefficient involving
derivative.
half-linear Euler differential equation
$$
\bigl(\Phi(x')\bigr)'+\frac{\gamma_p}{t^p}\Phi(x)=0,\quad
\Phi(x):=|x|^{p-2}x,\ \gamma_p:=\left(\frac{p-1}{p}\right)^p.
$$
A perturbation is also allowed in the coefficient involving
derivative.
Full Text:
PDFDOI: https://doi.org/10.2478/tatra.v48i0.96