Results 241 to 250 of about 5,648,332 (271)

Nonoscillation of half‐linear dynamic equations on time scales

Mathematical Methods in the Applied Sciences, 2021
The research contained in this paper belongs to the qualitative theory of dynamic equations on time scales. Via the detailed analysis of solutions of the associated Riccati equation and an advanced averaging technique, we provide the description of domain of nonoscillation of very general equations. The results are formulated and proved for half‐linear
Petr Hasil, Jozef Kisel'ák, Michal Pospíšil, Michal Veselý   +3 more
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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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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

On Recessive and Dominant Solutions for Half-linear Difference Equations

Journal of Difference Equations and Applications, 2004
Recessive and dominant solutions for the half-linear difference equation where \Phi _{p}(u) = \vert u \vert ^{p - 2}u with p > 1, {a n } and {b n } are positive real sequences for n \qeq 1, are studied. By the unique solvability of certain boundary value problems, recessive solutions are defined as “smallest solutions in a neighbourhood of infinity ...
M. CECCHI, Z. DOSLA, MARINI, MAURO
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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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Asymptotic formulae for solutions of half-linear differential equations

Applied Mathematics and Computation, 2017
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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A nonoscillation theorem for half-linear differential equations with periodic coefficients

Applied Mathematics and Computation, 2008
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jitsuro Sugie, Kouhei Matsumura
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Integral condition for oscillation of half-linear differential equations with damping

Applied Mathematics Letters, 2018
The authors study the second-order nonlinear differential equation \[ (\Phi_p(x'))'+a(t)\Phi_p(x')+b(t)\Phi_p(x)=0, \tag{1} \] where \(a\) and \(b\) are locally integrable functions on \([0,\infty)\) and \(\Phi_p\) is a real-valued function defined by \[ \Phi_p(z)=\left\{ \begin{array}{cl} \displaystyle |z|^{p-2}z &\;\text{if}\; z\neq 0,\\ 0 &\;\text ...
Jitsuro Sugie, Kazuki Ishibashi
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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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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
openaire   +2 more sources