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Modified Riccati technique for half-linear differential equations with delay [PDF]

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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Oscillation criteria for perturbed half-linear differential equations [PDF]

Electronic Journal of Qualitative Theory of Differential Equations
Oscillatory properties of perturbed half-linear differential equations are investigated. We make use of the modified Riccati technique. A certain linear differential equation associated with the modified Riccati equation plays an important part. Improved
Manabu Naito
doaj   +6 more sources

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
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Local estimates for modified Riccati equation in theory of half-linear differential equation [PDF]

Electronic Journal of Qualitative Theory of Differential Equations, 2012
In this paper we study the half-linear differential equation \begin{equation*} \bigl(r(t)\Phi_p(x')\bigr)'+c(t)\Phi_p(x)=0, \end{equation*} where $\Phi_p(x)=|x|^{p-2}x$, $p>1$. Using modified Riccati technique and suitable local estimates for terms
Simona Fišnarová, Robert Marik
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Euler Type Half-Linear Differential Equation with Periodic Coefficients [PDF]

Abstract and Applied Analysis, 2013
We investigate oscillatory properties of the perturbed half-linear Euler differential equation. We show that the results of the recent paper by O. Došlý and H.
Ondřej Došlý, Hana Funková
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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
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Hille-Nehari type oscillation and nonoscillation criteria for linear and half-linear differential equations [PDF]

MATEC Web of Conferences, 2019
Differential equations attract considerable attention in many applications. In particular, it was found out that half-linear differential equations behave in many aspects very similar to that in linear case. The aim of this contribution is to investigate
Rˇ eznícˇková Jana
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Solutions of half-linear differential equations in the classes Gamma and Pi [PDF]

Differential and Integral Equations, 2016
We study asymptotic behavior of (all) positive solutions of the non-oscillatory half-linear differential equation of the form (r(t)|y'|^ {alpha-1} sgn y')'=p(t)|y|^{alpha-1}sgn y, where alpha>1 and r,p are positive continuous functions, with the ...
Rehak, Pavel, TADDEI, Valentina
core   +4 more sources

Half-linear Euler differential equation and its perturbations [PDF]

Electronic Journal of Qualitative Theory of Differential Equations, 2016
We investigate oscillatory properties of perturbed half-linear Euler differential equation. We give an alternative proof (simpler and more straightforward) of the main result of [O. Došlý, H. Funková, Abstr. Appl. Anal. 2012, Art. ID 738472] and we prove
Ondrej Dosly
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Solutions of Riemann–Weber type half-linear differential equation [PDF]

Archivum Mathematicum, 2017
The author considers the Riemann-Weber type half-linear equation of the form \[(r(t)\Phi(x'))'+\left(c(t)+\frac{\mu}{h^p(t)(\int^t R^{-1}(s)ds)^2R(t)}\right)\Phi(x)=0,\] which is understood as a perturbation of the equation \((r(t)\Phi(x'))'+c(t)\Phi(x)=0\).
O. Doslý
openaire   +2 more sources