Oscillation of Half-Linear Differential Equations with Delay [PDF]
Abstract and Applied Analysis, 2013 We study the half-linear delay differential equation , , We establish a new a priori bound for the nonoscillatory solution of this equation and utilize this bound to derive new oscillation criteria for this equation in terms of oscillation criteria for ...
Simona Fišnarová, Robert Mařík
doaj +6 more sources
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
doaj +3 more sources
Asymptotic properties for half-linear difference equations [PDF]
Mathematica Bohemica, 2006 summary:Asymptotic properties of the half-linear difference equation \[ \Delta (a_{n}|\Delta x_{n}|^{\alpha }\mathop {\mathrm sgn}\Delta x_{n} )=b_{n}|x_{n+1}|^{\alpha }\mathop {\mathrm sgn}x_{n+1} \qquad \mathrm{(*)}\] are investigated by means of some ...
Cecchi, Mariella +3 more
core +4 more sources
Linearization technique for oscillation of perturbed half-linear differential equations [PDF]
Mathematica Bohemica, 2005 summary:It is shown that oscillation of perturbed second order half-linear differential equations can be derived from oscillation of second order linear differential equations associated with modified Riccati equations.
Naito, Manabu
core +5 more sources
Variational method and conjugacy criteria for half-linear differential equations [PDF]
Rocky Mountain Journal of Mathematics, 2013 summary:We establish new conjugacy criteria for half-linear second order differential equations. These criteria are based on the relationship between conjugacy of the investigated equation and nonpositivity of the associated energy ...
Chvátal, Martin +3 more
core +3 more sources
Two-Parametric Conditionally Oscillatory Half-Linear Differential Equations [PDF]
Abstract and Applied Analysis, 2011 We study perturbations of the nonoscillatory half-linear differential equation (r(t)Φ(x'))'+c(t)Φ(x)=0, Φ(x):=|x|p-2x, p>1. We find explicit formulas for the functions r̂, ĉ such that the equation [(r(t)+λr̂(t))Φ(x')]'+[c(t)+μĉ(t)]Φ(x)=0 is ...
Ondřej Došlý, Simona Fišnarová
doaj +3 more sources
Euler type linear and half-linear differential equations and their non-oscillation in the critical oscillation case [PDF]
Journal of Inequalities and Applications, 2019 This paper is devoted to the analysis of the oscillatory behavior of Euler type linear and half-linear differential equations. We focus on the so-called conditional oscillation, where there exists a borderline between oscillatory and non-oscillatory ...
Zuzana Došlá +3 more
doaj +2 more sources
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.
Simona Fišnarová, Robert Mařík
doaj +3 more sources
Reduction of order in the oscillation theory of half-linear differential equations
Electronic Journal of Qualitative Theory of Differential Equations, 2020 Oscillation of solutions of even order half-linear differential equations of the form \begin{equation*}\label{eq_Jaros} (\alpha_n,\dots,\alpha_1)x + q(t) |x|^\beta \operatorname{sgn} x = 0, \qquad t \geq a > 0, \tag{*} \end{equation*} where $\alpha_i ...
Jaroslav Jaroš
doaj +2 more sources
Oscillation Criteria for Advanced Half-Linear Differential Equations of Second Order
Mathematics, 2023 In this paper, we find new oscillation criteria for second-order advanced functional half-linear differential equations. Our results extend and improve recent criteria for the same equations established previously by several authors and cover the ...
Taher S. Hassan +2 more
doaj +3 more sources