Results 11 to 20 of about 7,785,042 (211)

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.
Migda, Małgorzata, Migda, Janusz
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Nonoscillatory Solutions to Higher-Order Nonlinear Neutral Dynamic Equations [PDF]

Symmetry, 2019
For a class of nonlinear higher-order neutral dynamic equations on a time scale, we analyze the existence and asymptotic behavior of nonoscillatory solutions on the basis of hypotheses that allow applications to equations with different integral convergence and divergence of the reciprocal of the coefficients.
Yang-Cong Qiu, Irena Jadlovská, Dhaou Lassoued, Tongxing Li   +3 more
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Existence of a nonoscillatory solution of a second-order linear neutral difference equation

Applied Mathematics Letters, 2007
Consider the neutral delay difference equation with positive and negative coefficients, Δ 2 ( x n + p x n − m ) + p n x n − k − q n x n − l = 0 , where p ∈ R and m , k , l ∈ N and p n , q n ∈ R + , n ≥ n 0 ∈ N .
Jinfa Cheng
semanticscholar   +1 more source

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.
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Nonoscillatory solutions of neutral delay differential equations [PDF]

Bulletin of the Australian Mathematical Society, 1993
Consider the following neutral delay differential equationwherep∈R,τ∈ (0, ∞), δ ∈R+= (0, ∞) and Q ∈ (C([t0, ∞),R). We show that ifthen Equation (*)has a nonoscillatory solution whenp≠ –1. We also deal in detail with a conjecture of Chuanxi, Kulenovic and Ladas, and Györi and Ladas.
Chen, Ming-Po, Yu, J. S., Wang, Z. C.
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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

On the nonoscillatory phase function for Legendre's differential equation [PDF]

Journal of Computational Physics, 2017
We express a certain complex-valued solution of Legendre's differential equation as the product of an oscillatory exponential function and an integral involving only nonoscillatory elementary functions.
J. Bremer, V. Rokhlin
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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
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Existence of Nonoscillatory Solution of Second Order Linear Neutral Delay Equation

, 1998
Consider the neutral delay differential equation with positive and negative coefficients,[formula]wherep ∈ Rand[formula] Some sufficient conditions for the existence of a nonoscillatory solution of the above equation expressed in terms of ∫∞ sQi(s) ds
M. Kulenović, S. Hadžiomerspahić
semanticscholar   +1 more source

Principal Solutions Revisited [PDF]

, 2015
The main objective of this paper is to identify principal solutions associated with Sturm-Liouville operators on arbitrary open intervals $(a,b) \subseteq \mathbb{R}$, as introduced by Leighton and Morse in the scalar context in 1936 and by Hartman in ...
Clark, Stephen, Gesztesy, Fritz, Nichols, Roger   +2 more
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