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.
openaire +2 more sources
Oscillation of second order half-linear difference equations (I)
Applied Mathematical Sciences, 2011 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jiang, Jianchu, Tang, Xianhua
openaire +2 more sources
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
doaj +1 more source
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
doaj +1 more source
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
openaire +3 more sources
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
doaj +1 more source
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
doaj +1 more source
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
doaj +1 more source
Quantum-mechanical effects in a linear time-dependent potential
, 2009 The solution of the time-dependent Schr\"odinger equation is discussed for a particle confined in half-space $x>0$ with a linear potential $V(x)=Kx$ in the following situations: (a) sudden removal of the wall and switching on the linear potential $V(x ...
Mousavi, S. V.
core +1 more source
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
core +1 more source