TY  - JOUR
ID  - Naito2021
LB  - Naito2021
AU  - Naito, Manabu
TI  - Remarks on the existence of nonoscillatory solutions of half-linear ordinary differential equations, I
ST  - Remarks on the existence of nonoscillatory solutions of half-linear ordinary differential equations, I
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2021
VL  - 41
IS  - 1
SP  - 71
EP  - 94
DO  - https://doi.org/10.7494/OpMath.2021.41.1.71
UR  - https://doi.org/10.7494/OpMath.2021.41.1.71
AB  - We consider the half-linear differential equation of the form \[(p(t)|x'|^{\alpha}\mathrm{sgn} x')' + q(t)|x|^{\alpha}\mathrm{sgn} x = 0, \quad t\geq t_{0},\] under the assumption \(\int_{t_{0}}^{\infty}p(s)^{-1/\alpha}ds =\infty\). It is shown that if a certain condition is satisfied, then the above equation has a pair of nonoscillatory solutions with specific asymptotic behavior as \(t \to \infty\).
KW  - asymptotic behavior
KW  - nonoscillatory solution
KW  - half-linear differential equation
KW  - Hardy-type inequality
SN  - 1232-9274
ER  -