Results 1 to 10 of about 494 (181)

Nonoscillatory Solutions to Second-Order Neutral Difference Equations [PDF]

Symmetry, 2018
We study asymptotic behavior of nonoscillatory solutions to second-order neutral difference equation of the form: Δ ( r n Δ ( x n + p n x n − τ ) ) = a n f ( n , x n ) + b n . The obtained results are based on the discrete Bihari type lemma and a Stolz type lemma.
Janusz Migda, Malgorzata Migda, Migda Małgorzata   +2 more
exaly   +2 more sources

Nonoscillatory solutions of the four-dimensional difference system

Electronic Journal of Qualitative Theory of Differential Equations, 2012
We study asymptotic properties of nonoscillatory solutions for a four-dimensional system \[\begin{aligned} \Delta x_{n}&= C_{n}\, y_{n}^{\frac{1}{\gamma}} \\ \Delta y_{n}&= B_{n}\, z_{n}^{\frac{1}{\beta}} \\ \Delta z_{n}&= A_{n}\, w_{n}^{\frac{1}{\alpha}}
Zuzana Dosla, J. Krejčová
doaj   +2 more sources

New Criteria for Sharp Oscillation of Second-Order Neutral Delay Differential Equations

Mathematics, 2021
In this paper, new oscillation criteria for second-order half-linear neutral delay differential equations are established, using a recently developed method of iteratively improved monotonicity properties of a nonoscillatory solution. Our approach allows
Irena Jadlovská
doaj   +1 more source

Oscillation and Asymptotic Behavior of Three-Dimensional Third-Order Delay Systems

International Journal of Differential Equations, 2023
In this paper, oscillation and asymptotic behavior of three-dimensional third-order delay systems are discussed. Some sufficient conditions are obtained to ensure that every solution of the system is either oscillatory or nonoscillatory and converges to ...
Ahmed Abdulhasan Naeif, Hussain Ali Mohamad   +1 more
doaj   +1 more source

On nonoscillatory solutions of differential inclusions [PDF]

Proceedings of the American Mathematical Society, 2002
This paper introduces a nonoscillatory theory for differential inclusions based on fixed point theory for multivalued maps.
Agarwal, R.P., Grace, S.R., O'Regan, D.
openaire   +1 more source

Oscillation and Nonoscillatory Criteria of Higher Order Dynamic Equations on Time Scales

Mathematics, 2022
In this paper, we consider two universal higher order dynamic equations with several delay functions. We will establish two oscillatory criteria of the first equation and a sufficient and necessary condition for the second equation with a nonoscillatory ...
Ya-Ru Zhu, Zhong-Xuan Mao, Jing-Feng Tian, Ya-Gang Zhang, Xin-Ni Lin   +4 more
doaj   +1 more source

On nonoscillatory solutions of a nonlinear differential equation [PDF]

Proceedings of the American Mathematical Society, 1972
Sufficient conditions are given which insure that all nonoscillatory solutions of (p(t)x')'+h(x)x'+q(t)g(x) =f (t) tend to zero as t tends to infinity. In this paper we examine the behavior of the nonoscillatory solutions of the equation (1) (p(t)x')' + h(x)x' + q(t)g(x) = f(t) where p, q, andf are real valued and continuous for t >0 and h and g are ...
openaire   +2 more sources

Nonoscillatory solutions for discrete equations

Computers & Mathematics with Applications, 2003
The authors consider the discrete equation \[ \Delta(a(k)\Delta(y(k)+ py(k-\tau)))+F(k+1,y(k+1-\sigma))=0 \quad (k\in{\mathbb N}), \] here \(\Delta\) is the difference operator, \(F\) is a continuous map from \({\mathbb N}\times (0,\infty)\) into \([0,\infty), \tau,\sigma\in{\mathbb N}\cup\{0\}, a:{\mathbb N}\to(0,\infty)\), and \(p\in{\mathbb R}\).
Agarwal, R.P., Grace, S.R., O'Regan, D.
openaire   +1 more source

Existence and asymptotic behavior of nonoscillatory solutions of half-linear ordinary differential equations [PDF]

Opuscula Mathematica, 2023
We consider the half-linear differential equation \[(|x'|^{\alpha}\mathrm{sgn}\,x')' + q(t)|x|^{\alpha}\mathrm{sgn}\,x = 0, \quad t \geq t_{0},\] under the condition \[\lim_{t\to\infty}t^{\alpha}\int_{t}^{\infty}q(s)ds = \frac{\alpha^{\alpha}}{(\alpha+1)^
Manabu Naito
doaj   +1 more source

A note on the existence of solutions with prescribed asymptotic behavior for half-linear ordinary differential equations [PDF]

Mathematica Bohemica
The half-linear differential equation (|u'|^{\alpha}{\rm sgn} u')' = \alpha(\lambda^{\alpha+ 1} + b(t))|u|^{\alpha}{\rm sgn} u, \quad t \geq t_0, is considered, where $\alpha$ and $\lambda$ are positive constants and $b(t)$ is a real-valued ...
Manabu Naito
doaj   +1 more source