Asymptotic behaviour at infinity of solutions of second kind integral equations on unbounded regions of Rn [PDF]
, 1994 We consider second kind integral equations of the form x(s) - (abbreviated x - K x = y ), in which Ω is some unbounded subset of Rn. Let Xp denote the weighted space of functions x continuous on Ω and satisfying x (s) = O(|s|-p ),s → ∞We show that if the
Peplow, AT, Chandler-Wilde, SN
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Conjugacy and principal solution of generalized half-linear second order differential equations
Electronic Journal of Qualitative Theory of Differential Equations, 2012 We study the generalized half-linear second order differential equation and the associated Riccati type differential equation. We introduce the concepts of minimal and principal solutions of these equations and using these concepts we prove a new ...
Ondrej Dosly, J. Reznickova
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Leza Mesiah, Half the Sky, 1980-1986
, 1984 December 1984, Volume II, Number 12 edition of a Newsletter for Half the Sky Newsletter.
Half the Sky
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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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Modified Riccati technique for half-linear differential equations with delay
Electronic Journal of Qualitative Theory of Differential Equations, 2014 We study the half-linear differential equation $$ (r(t)\Phi(x'(t)))'+c(t)\Phi(x(\tau(t)))=0,\quad \Phi(x):=|x|^{p-2}x,\ p>1. $$ We formulate new oscillation criteria for this equation by comparing it with a certain ordinary linear or half-linear ...
Simona Fišnarová, Robert Marik
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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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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 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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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 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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