Results 301 to 310 of about 268,617 (332)

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.
Kandelaki, N., Lomtatidze, A., Ugulava, D.   +2 more
openaire   +2 more sources

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

Oscillation criteria for second-order half-linear differential equations

Mathematical and Computer Modelling, 1999
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exaly   +3 more sources

Nonoscillation and oscillation of second order half-linear differential equations

Journal of Mathematical Analysis and Applications, 2007
We study the oscillation problems for the second order half-linear differential equation [p(t)Φ(x′)]′+q(t)Φ(x)=0, where Φ(u)=|u|r−1u with r>0, 1/p and q are locally integrable on R+; p>0, q⩾0 a.e. on R+, and ∫0∞p−1/r(t)dt=∞. We establish new criteria for
Qingkai Kong
exaly   +2 more sources

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
exaly   +3 more sources

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

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
openaire   +1 more source

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
openaire   +1 more source