Results 281 to 290 of about 735,542 (308)

A half-linear differential equation and variational problem

Nonlinear Analysis: Theory, Methods & Applications, 2001
The author investigates the variational problem with general boundary conditions whose corresponding Euler-Lagrange equation is the half-linear differential equation \[ (r(t)\Phi(y'))'+q(t)\Phi(y)=0, \] with \(\Phi(u)=|u|^{p-2}u\), \(p>1\) a constant, \(r,q\) real-valued continuous functions defined on a compact interval \(I=[a,b]\), and \(r(t)>0\) on \
R. Mařík
openaire   +3 more sources

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.
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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   +3 more sources

Interval oscillation of second-order half-linear functional differential equations

Applied Mathematics and Computation, 2004
By employing an inequality due to Hardy, Littlewood and Polya and averaging techniques, new interval oscillation criteria are established for the second-order half-linear functional-differential equation \[ \Big[r(t)| y'(t)| ^{\alpha-1} y'(t)\Big]'+q(t)| y(\tau(t))| ^{\alpha-1}y(\tau(t))=0. \] The presented results show that the term \(\tau(t)=t\pm\tau\
Wan‐Tong Li
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Exponential estimates for solutions of half-linear differential equations

Acta Mathematica Hungarica, 2015
The paper studies the half-linear differential equation \[ \left(\Phi(y')\right)'=p(t) \Phi(y), \tag{(1)} \] where the function \(p\) is continuous and nonnegative on \([0,\infty)\) and the function \(\Phi\) has the form \[ \Phi(u)=| u| ^{\alpha-1} \text{sgn}\;u, \quad \alpha>1.
P. Řehák
openaire   +4 more sources

"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

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
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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
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Comparison techniques for detection of nonoscillation in half‐linear differential equations of the second order

Mathematische Nachrichten
We present a new comparison method which improves the classical Hille–Wintner theorem and its generalization to a pair of half‐linear differential equations of the second order by incorporating a solution of the Riccati‐type equation associated with the ...
J. Jaros
semanticscholar   +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