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Existence and asymptotic behavior of nonoscillatory solutions of half-linear ordinary differential equations

Naito Manabu

Opuscula Mathematica

2023

Vol. 43, no. 2

221--246

We consider the half-linear differential equation (|x′|αsgn x′)′ + q(t)|x|αsgn x = 0, t ≥ t0, under the condition [formula] 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 → ∞.

Remarks on the existence of nonoscillatory solutions of half-linear ordinary differential equations, I

Naito Manabu

Opuscula Mathematica

2021

Vol. 41, no. 1

71--94

We consider the half-linear differential equation of the form [formula], under the assumption [formula]. 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 →∞.