Results 231 to 240 of about 58,243 (254)

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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A nonoscillation theorem for half-linear differential equations with periodic coefficients

Applied Mathematics and Computation, 2008
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Jitsuro Sugie, Kouhei Matsumura
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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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Oscillation and Nonoscillation of Half-Linear Differential Equations

2002
In this chapter we shall present oscillation and nonoscillation criteria for second order half-linear differential equations. In recent years these equations have attracted considerable attention. This is largely due to the fact that half-linear differential equations occur in a variety of real world problems; moreover, these are the natural ...
Ravi P. Agarwal, Said R. Grace, Donal O’Regan   +2 more
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On the half-linear second order differential equations

Acta Mathematica Hungarica, 1987
\textit{I. Bihari} [Publ. Math. Inst. Hungar. Acad. Sci. 2, 159-172 (1958; Zbl 0089.068)] defined the half-linear second order differential equation (1) \((p(t)x')'+q(t)f(x,p(t)x')=0\) for the unknown function \(x=x(t)\) where the functions p(t), q(t) are continuous on some interval \(I=[a,b)\) \((- \infty 0\) if \(x\neq 0\) (consequently \(f(0,y)=0 ...
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Oscillation and asymptotics for second-order half-linear differential equations

Applied Mathematics and Computation, 2001
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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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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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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\
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Nonoscillation of the Mathieu-type half-linear differential equation and its application to the generalized Whittaker–Hill-type equation

Monatshefte Fur Mathematik, 2022
Kazuki Ishibashi
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