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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Non-mean-field Critical Exponent in a Mean-field Model : Dynamics versus Statistical Mechanics [PDF]
, 2014 The mean-field theory tells that the classical critical exponent of susceptibility is the twice of that of magnetization. However, the linear response theory based on the Vlasov equation, which is naturally introduced by the mean-field nature, makes the ...
Ogawa, Shun +2 more
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On the integral characterization of principal solutions for half-linear ODE
Electronic Journal of Qualitative Theory of Differential Equations, 2013 We discuss a new integral characterization of principal solutions for half-linear differential equations, introduced in the recent paper of S. Fisnarova and R. Marik, Nonlinear Anal. 74 (2011), 6427-6433.
M. Cecchi +3 more
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Diffusion approximations and domain decomposition method of linear transport equations: asymptotics and numerics [PDF]
, 2015 In this paper we construct numerical schemes to approximate linear transport equations with slab geometry by diffusion equations. We treat both the case of pure diffusive scaling and the case where kinetic and diffusive scalings coexist.
Li, Qin, Lu, Jianfeng, Sun, Weiran
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On conjugacy of second-order half-linear differential equations on the real axis
Electronic Journal of Qualitative Theory of Differential Equations, 2016 Some conjugacy criteria are given for the equation $$ \big(|u'|^{\alpha}\operatorname{sgn}u'\big)'+p(t)|u|^{\alpha}\operatorname{sgn} u=0, $$ where $p\colon\mathbb{R} \to \mathbb{R}$ is a locally integrable function and $\alpha>0$, which generalise and ...
Jiří Šremr
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The Forced Non-Linear Schroedinger Equation with a Potential on the Half-Line
, 2003 In this paper we prove that the initial-boundary value problem for the forced non-linear Schroedinger equation with a potential on the half-line is locally and (under stronger conditions) globally well posed, i.e.
Adams +18 more
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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 Theorems for Second-Order Half-Linear Advanced Dynamic Equations on Time Scales
International Journal of Differential Equations, 2011 This paper is concerned with the oscillatory behavior of the second-order half-linear advanced dynamic equation (𝑟(𝑡)(𝑥Δ(𝑡))𝛾)Δ+𝑝(𝑡)𝑥𝛾(𝑔(𝑡))=0 on an arbitrary time scale 𝕋 with sup 𝕋=∞, where 𝑔(𝑡)≥𝑡 and ∫∞𝑡𝑜(Δ𝑠/(𝑟1/𝛾(𝑠)))
Shuhong Tang +2 more
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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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The Bohl spectrum for nonautonomous differential equations [PDF]
, 2016 We develop the Bohl spectrum for nonautonomous linear differential equation on a half line, which is a spectral concept that lies between the Lyapunov and the Sacker--Sell spectrum.
Doan, Thai Son +2 more
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