Integral Comparison Criteria for Half-Linear Differential Equations Seen as a Perturbation [PDF]
Mathematics, 2021 In this paper, we present further developed results on Hille–Wintner-type integral comparison theorems for second-order half-linear differential equations.
Zuzana Pátíková
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Electronic Journal of Qualitative Theory of Differential Equations, 2016 We study the half-linear neutral differential equation \begin{equation*} \Bigl[r(t)\Phi(z'(t))\Bigr]'+c(t)\Phi(x(\sigma(t)))=0, \qquad z(t)=x(t)+b(t)x(\tau(t)), \end{equation*} where $\Phi(t)=|t|^{p-2}t$.
Simona Fišnarová
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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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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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Oscillations of half-linear second order differential equations
Hiroshima Mathematical Journal, 1995 Let \(\varphi:\mathbb{R}\to\mathbb{R}\) be defined by \(\varphi(s)=|s|^{p-2}s\), with \(p>1\) a fixed number. We extend Sturm's comparison theorem of the linear differential equation \[ {\textstyle {\frac{d}{dt}}} [r(t)u'(t)]+ c(t)u(t)=0 \] to the nonlinear differential equation \[ {\textstyle {\frac{d}{dt}}} \{r(t)\varphi(u'(t))\}+ c(t)\varphi(u(t))=0,
Li, Horng Jaan, Yeh, Cheh Chih
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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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Principal solution of half-linear differential equation: Limit and integral characterization
Electronic Journal of Qualitative Theory of Differential Equations, 2008 We investigate integral and limit characterizations of the principal solution of the nonoscillatory half-linear differential equation $$ (r(t)\Phi(x'))'+c(t)\Phi(x)=0,\quad \Phi(x)=|x|^{p-2},\ p>1 $$.
Zuzana Dosla, Ondrej Dosly
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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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New Oscillation Results For Third-Order Half-Linear Neutral Differential Equations [PDF]
Mathematics, 2020 The main purpose of this paper is to obtain criteria for the oscillation of all solutions of a third-order half-linear neutral differential equation.
K. S. Vidhyaa +2 more
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Oscillation of modified Euler type half-linear differential equations via averaging technique
Electronic Journal of Differential Equations, 2022 In this article, we analyze the oscillation behavior of half-linear differential equation $$\big( r(t) t^{p-1} \Phi(x')\big)' + \frac{s(t)}{t \log^pt} \Phi(x) = 0, \quad \Phi(x)=|x|^{p-1}\text{sgn} x, \quad p > 1.
P. Hasil, J. Šišoláková, M. Veselý
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