Results 21 to 30 of about 6,725,901 (296)

Asymptotic Behavior of Solutions to Half-Linear q-Difference Equations [PDF]

Abstract and Applied Analysis, 2011
We derive necessary and sufficient conditions for (some or all) positive solutions of the half-linear q-difference equation Dq(Φ(Dqy(t)))+p(t)Φ(y(qt))=0, t∈{qk:k∈N0} with q>1, Φ(u)=|u|α−1sgn⁡u with α>1, to behave like
Pavel Řehák
doaj   +4 more sources

Oscillation Criteria Enhanced for Advanced Half-Linear Dynamic Equations

Journal of Mathematics
The purpose of this study is to develop new iterative oscillation criteria for second-order half-linear advanced dynamic equations. These findings improve and extend recently established criteria for the same equation by several authors as well as ...
Taher S. Hassan, Elmetwally M. Elabbasy, Naveed Iqbal, Akbar Ali, Khudhayr A. Rashedi, Amir Abdel Menaem   +5 more
doaj   +2 more sources

Oscillation criteria for perturbed half-linear differential equations

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   +3 more sources

Kneser-type oscillation criteria for second-order half-linear advanced difference equations [PDF]

Opuscula Mathematica, 2022
The authors present Kneser-type oscillation criteria for a class of advanced type second-order difference equations. The results obtained are new and they improve and complement known results in the literature. Two examples are provided to illustrate the
N. Indrajith, John R. Graef, E. Thandapani   +2 more
doaj   +1 more source

Oscillation and Asymptotic Properties of Second Order Half-Linear Differential Equations with Mixed Deviating Arguments

Mathematics, 2021
In this paper, we study oscillation and asymptotic properties for half-linear second order differential equations with mixed argument of the form r(t)(y′(t))α′=p(t)yα(τ(t)).
B. Baculíková
semanticscholar   +1 more source

Oscillation of half-linear differential equations with mixed type of argument

Electronic Journal of Qualitative Theory of Differential Equations, 2022
This paper is devoted to the study of the oscillatory behavior of half-linear functional differential equations with deviating argument of the form ( E )
J. Džurina, B. Baculíková
semanticscholar   +1 more source

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 }\text{sgn}\, \Delta x_{n} )=b_{n}| x_{n+1}| ^{\alpha }\text{sgn}\, x_{n+1} \tag{\(*\)} \] are investigated by means of some summation criteria.
M. CECCHI, Z. DOSLA, MARINI, MAURO, I. VRKOC   +3 more
openaire   +3 more sources

Use of the Modified Riccati Technique for Neutral Half-Linear Differential Equations

Mathematics, 2021
We study the second-order neutral half-linear differential equation and formulate new oscillation criteria for this equation, which are obtained through the use of the modified Riccati technique. In the first statement, the oscillation of the equation is
Z. Pátíková, Simona Fisnarová
semanticscholar   +1 more source

A sharp oscillation result for second-order half-linear noncanonical delay differential equations

Electronic Journal of Qualitative Theory of Differential Equations, 2020
In the paper, new single-condition criteria for the oscillation of all solutions to a second-order half-linear delay differential equation in noncanonical form are obtained, relaxing a traditionally posed assumption that the delay function is ...
Jozef Džurina, Irena Jadlovská
doaj   +1 more source

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, Takaŝi, Kusano, Tanigawa, Tomoyuki   +2 more
openaire   +1 more source