Remarks on the existence of nonoscillatory solutions of half-linear ordinary differential equations, I
Remarks on the existence of nonoscillatory solutions of half-linear ordinary differential equations, I
复制标题
关于半线性常微分方程非振荡解存在性的评述，I
DOI：
10.7494/opmath.2021.41.1.71
复制
发表时间：
2021
期刊：
影响因子：
--
通讯作者：
Manabu Naito
中科院分区：
文献类型：
--
作者：
Manabu Naito
我们在假设\(\int_{t_{0}}^{\infty}p(s)^{-1/\alpha}ds =\infty\)下考虑形式为\[(p(t)|x'|^{\alpha}\mathrm{sgn} x')' + q(t)|x|^{\alpha}\mathrm{sgn} x = 0, \quad t\geq t_{0},\]的半线性微分方程。结果表明，如果满足某一条件，则上述方程有一对具有特定渐近行为的非振荡解\(t \to \infty\)。
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 \(t \to \infty\).