Results 231 to 240 of about 612,872 (266)

Nonoscillatory half-linear differential equations and generalized Karamata functions

Nonlinear Analysis: Theory, Methods & Applications, 2006
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Jaroš, Jaroslav, Takaŝi, Kusano, Tanigawa, Tomoyuki   +2 more
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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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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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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.
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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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Oscillation of Second-Order Half-Linear Neutral Advanced Differential Equations

Communications on Applied Mathematics and Computation, 2020
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Shi, Shan, Han, Zhenlai
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Poincaré-Perron problem for half-linear ordinary differential equations

Differential and Integral Equations
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Manabu, Naito, Usami, Hiroyuki
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Conjugacy of half-linear second-order differential equations

Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 2000
Focal point and conjugacy criteria for the half-linear second-order differential equation are obtained using the generalized Riccati transformation. An oscillation criterion is given in case when the function c(t) is periodic.
Došlý, Ondřej, Elbert, Árpád
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Oscillation of Second Order Half-Linear Differential Equations with Damping

gmj, 2003
Abstract This paper is concerned with a class of second order half-linear damped differential equations. Using the generalized Riccati transformation and the averaging technique, new oscillation criteria are obtained which are either extensions of or complementary to a number of the existing results.
Yang, Qigui, Cheng, Sui Sun
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