TY  - JOUR
ID  - Naito2023
LB  - Naito2023
AU  - Naito, Manabu
TI  - Existence and asymptotic behavior of nonoscillatory solutions of half-linear ordinary differential equations
ST  - Existence and asymptotic behavior of nonoscillatory solutions of half-linear ordinary differential equations
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2023
VL  - 43
IS  - 2
SP  - 221
EP  - 246
DO  - https://doi.org/10.7494/OpMath.2023.43.2.221
UR  - https://doi.org/10.7494/OpMath.2023.43.2.221
AB  - We consider the half-linear differential equation \[(|x'|^{\alpha}\mathrm{sgn}\,x')' + q(t)|x|^{\alpha}\mathrm{sgn}\,x = 0, \quad t \geq t_{0},\] under the condition \[\lim_{t\to\infty}t^{\alpha}\int_{t}^{\infty}q(s)ds = \frac{\alpha^{\alpha}}{(\alpha+1)^{\alpha+1}}.\] It is shown that if certain additional conditions are 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
SN  - 1232-9274
ER  -