Results 11 to 20 of about 58,243 (254)
The oscillation of half-linear differential equations with an oscillatory coefficient
Mathematical and Computer Modelling, 1996 The authors derive lower bounds for the distance between consecutive zeros of a solution of the second-order half-linear differential equation \[ \Bigl(| y'(t)| ^{\alpha -1}y'(t)\Bigr)'+q(t)| y(t)| ^{\alpha -1}y(t)=0, \tag{*} \] where \(q(t):[t_0,\infty)\to\mathbb{R}\) is locally integrable for some \(t_0\geq 0\) and \(\alpha >0\) is a constant.
Hong, Huei-Lin +2 more
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Hille-Nehari type oscillation and nonoscillation criteria for linear and half-linear differential equations [PDF]
MATEC Web of Conferences, 2019 Differential equations attract considerable attention in many applications. In particular, it was found out that half-linear differential equations behave in many aspects very similar to that in linear case. The aim of this contribution is to investigate
Rˇ eznícˇková Jana
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Existence and asymptotic behavior of nonoscillatory solutions of half-linear ordinary differential equations [PDF]
Opuscula Mathematica, 2023 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)^
Manabu Naito
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On Constants in Nonoscillation Criteria for Half‐Linear Differential Equations [PDF]
Abstract and Applied Analysis, 2011 We study the half‐linear differential equation (r(t)Φ(x′)) ′ + c(t)Φ(x) = 0, where Φ(x) = |x|p−2x, p > 1. Using the modified Riccati technique, we derive new nonoscillation criteria for this equation. The results are closely related to the classical Hille‐Nehari criteria and allow to replace the fixed constants in known nonoscillation criteria by a ...
Simona Fišnarová, Robert Mařík
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Oscillation of Second Order Nonlinear Neutral Differential Equations
Mathematics, 2022 The study of the oscillatory behavior of solutions to second order nonlinear differential equations is motivated by their numerous applications in the natural sciences and engineering.
Yingzhu Wu, Yuanhong Yu, Jinsen Xiao
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Oscillation criteria for fourth order half-linear differential equations [PDF]
Archivum Mathematicum, 2020 In this paper, the following fourth-order differential equation \[(|y^{\prime\prime}|^{\alpha}\operatorname{sgn}(y^{\prime\prime}))^{\prime\prime}+q(t)|y|^{\alpha}\operatorname{sgn}(y)=0,\quad t\geq a>0\] is considered, where \(\alpha\) is a positive constant and \(q:[a,\infty)\to(0,\infty)\) is a continuous function.
Jaroš, Jaroslav +2 more
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ON CONNECTED HALF-LINEAR DIFFERENTIAL EQUATIONS
Demonstratio Mathematica, 1999 Summary: Relations among several classes of half-linear differential equations with or without delays are established. By means of these connections, the existence of eventually positive solutions can be inferred from the properties of either one of these families of equations.
Zhang, Guang, Cheng, Sui Sun
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A precise asymptotic description of half‐linear differential equations
Mathematische Nachrichten, 2023 AbstractWe study asymptotic behavior of solutions of nonoscillatory second‐order half‐linear differential equations. We give (in some sense optimal) conditions that guarantee generalized regular variation of all solutions, where no sign condition on the potential is assumed.
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Nonoscillation of higher order half-linear differential equations
Electronic Journal of Qualitative Theory of Differential Equations, 2015 We establish nonoscillation criteria for even order half-linear differential equations. The principal tool we use is the Wirtinger type inequality combined with various perturbation techniques.
Ondrej Dosly, Vojtěch Růžička
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Half-linear differential equations with oscillating coefficient
Differential and Integral Equations, 2005 n ...
M. CECCHI, Z. DOSLA, MARINI, MAURO
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