Results 181 to 190 of about 215,355 (212)

On Oscillation and Nonoscillation of a Second Order Half-Linear Equation

Georgian Mathematical Journal, 2000
Abstract New oscillation and nonoscillation criteria are established for the equation u″ + p(t)|u| α |u′|1–α sgn u = 0, where α ∈]0, 1] and the function p :]0, +∞[→] – ∞, +∞[ is locally integrable.
A Lomtatidze
exaly   +3 more sources

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 \
exaly   +3 more sources

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
openaire   +2 more sources

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

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
openaire   +2 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.
openaire   +2 more sources

Asymptotic formulae for solutions of half-linear differential equations

Applied Mathematics and Computation, 2017
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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

Nonoscillation and oscillation of second order half-linear difference equations

Applied Mathematics and Computation, 2008
Conditions of oscillatory and non-oscillatory behavior for the second order, half linear difference equation of the form \[ \Delta(| \Delta x_{n-1}| ^{r-1}\Delta x_{n-1}) + q_n| x_n| ^{r-1}x_n = 0,\quad r>0,\;q_n\geq 0 \] are given.
Yuan Gong Sun, Fan Wei Meng
openaire   +2 more sources