Browsing by Subject "half-linear differential equation"
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Item type:Article, Access status: Open Access , Existence and asymptotic behavior of nonoscillatory solutions of half-linear ordinary differential equations(Wydawnictwa AGH, 2023) Naito, ManabuWe 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 $t \to \infty$.Item type:Article, Access status: Open Access , Remarks on the existence of nonoscillatory solutions of half-linear ordinary differential equations, I(Wydawnictwa AGH, 2021) Naitō, ManabuWe 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 $t \to \infty$.