Results 251 to 260 of about 1,596,954 (307)

"New asymptotic results for half-linear differential equations with deviating argument"

Carpathian Journal of Mathematics, 2022
"In the paper, we study the oscillation of the half-linear second-order differential equations with deviating argument of the form \begin{equation*} \left(r(t)(y'(t))^{\alpha}\right)'=p(t)y^{\alpha}(\tau(t)).
B. Baculíková, J. Džurina
semanticscholar   +1 more source

Applications of the novel diamond alpha Hardy–Copson type dynamic inequalities to half linear difference equations

Journal of difference equations and applications (Print), 2022
This paper is devoted to novel diamond alpha Hardy–Copson type dynamic inequalities, which are complements of the classical ones obtained for and their applications to difference equations.
Z. Kayar, B. Kaymakçalan
semanticscholar   +1 more source

Conditionally oscillatory half-linear differential equations

Acta Mathematica Hungarica, 2008
The authors assume that a nonoscillatory solution to the half-linear equation \[ (r(t)\Phi(x'))+c(t)\Phi(x)=0,\;\Phi(x)=| x| ^{p-2}x,\;p>1, \] is known. Then they are able to construct a function \(d\) such that the (perturbed) equation \[ (r(t)\Phi(x'))+(c(t)+\lambda d(t))\Phi(x)=0 \] is conditionally oscillatory.
Došlý, O., Ünal, M.
openaire   +2 more sources

Nonoscillation in half-linear differential equations

Publicationes Mathematicae Debrecen, 1996
Necessary conditions are given for the nonoscillation of the solutions of the equation \[ [r(t)|u'(t)|^{p-2}u'(t)]'+c(t)|u(t)|^{p-2}u(t)=0, \] where \(p>1\) is a constant, and \(r(t)>0\).
Li, Horng-Jaan, Yeh, Cheh-Chih
openaire   +1 more source

Perturbations of the Half-Linear Euler Differential Equation

Results in Mathematics, 2000
The authors investigate oscillation/nonoscillation properties of the perturbed half-linear Euler differential equation \[ (x'{}^{n*})'+\frac{\gamma_0}{t^{n+1}}[n+2(n+1)\delta(t)]x^{n*}=0, \tag{*} \] where the function \(\delta(t)\) is piecewise continuous on \((t_0,\infty)\), \(t_0\geq 0\), \(n>0\) is a fixed real number and \(u^{n*}=|u|^n \text{sgn} u\
Elbert, Á., Schneider, A.
openaire   +2 more sources

Non‐oscillation of linear and half‐linear differential equations with unbounded coefficients

Mathematical methods in the applied sciences, 2020
We deal with Euler‐type half‐linear second‐order differential equations, and our intention is to derive conditions in order their non‐trivial solutions are non‐oscillatory. This paper connects to the article P. Hasil, J. Šišoláková, M.
J. Šišoláková
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Oscillation result for half‐linear dynamic equations on timescales and its consequences

Mathematical methods in the applied sciences, 2019
We study oscillatory properties of half‐linear dynamic equations on timescales. Via the combination of the Riccati technique and an averaging method, we find the domain of oscillation for many equations. The presented main result is not the conversion of
P. Hasil, M. Veselý
semanticscholar   +1 more source

Poincaré-Perron problem for half-linear ordinary differential equations

Differential and Integral Equations
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Manabu, Naito, Usami, Hiroyuki
openaire   +1 more source

Asymptotic behavior of solutions of half-linear differential equations and generalized Karamata functions

, 2020
We study the asymptotic behavior of eventually positive solutions of the second-order half-linear differential equation (p⁢(t)⁢|x′|α⁢sgn⁡x′)′+q⁢(t)⁢|x|α⁢sgn⁡x=0,(p(t)\lvert x^{\prime}\rvert^{\alpha}\operatorname{sgn}x^{\prime})^{\prime}+q(% t)\lvert x ...
K. Takaši, J. Manojlovic
semanticscholar   +1 more source

Lyapunov-Type Inequalities for Half-Linear Differential Equations

2021
In this chapter, we give a survey of the most basic results on Lyapunov-type inequalities for second-order, third-order, and higher-order half-linear differential equations and sketch some recent developments related to this type of inequalities.
Ravi P. Agarwal, Martin Bohner, Abdullah Özbekler   +2 more
openaire   +1 more source