Results 11 to 20 of about 2,861,683 (201)
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
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Nonoscillatory solutions of nonlinear differential systems
Computers & Mathematics with Applications, 2003 Here, the system of \(n\) ordinary differential equations \[ \begin{aligned} x'_i&=a_i(t)f_i(x_{i+1}), \qquad\text{for }i=1,\dots,n-1, \\ x'_n&=-a_n(t)f_n(x_1) \end{aligned} \] is studied. The functions \(a_i(t)\) are supposed to be positive and continuous on \([t_0,\infty)\) for \(i=1,\dots,n\), and the functions \(f_i(u)\) are supposed to be ...
Yang, Xiaojing
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Delay difference equations: Coexistence of oscillatory and nonoscillatory solutions [PDF]
Analysis, 2013 The aim of this work is to study the coexistence of oscillatory and nonoscillatory solutions of a certain scalar delay difference equation. © 2013, by Walter de Gruyter Berlin Boston.
Pinelas, Sandra +3 more
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Nonoscillatory Solutions of Higher-Order Fractional Differential Equations [PDF]
Mediterranean Journal of Mathematics, 2022 The authors study the asymptotic behaviour of the non-oscillatory solutions of forced fractional differential equations in the form \[ CD^{\alpha}_c y(t) + f_1(t, x(t)) = b(t) + k(t)x^{\beta}(t) + f_2(t, x(t)),\tag{1} \] where \[ y = \left(a (x^\prime)^\beta \right)^{(n-1)}, \qquad n \in\mathbb{N}, \] \(\beta \) is the ratio of two odd positive ...
Martin Bohner +3 more
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Existence of Nonoscillatory Solutions for System of Higher-Order Neutral Differential Equations with Distributed Deviating Arguments [PDF]
Discrete Dynamics in Nature and Society, 2013 In this paper, we consider the existence of nonoscillatory solutions for system of variable coefficients higher-order neutral differential equations with distributed deviating arguments.
Youjun Liu, Jianwen Zhang, Jurang Yan
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Nonoscillatory half-linear difference equations and recessive solutions [PDF]
Advances in Difference Equations, 2005 Recessive and dominant solutions for the nonoscillatory half-linear difference equation are investigated. By using a uniqueness result for the zero-convergent solutions satisfying a suitable final condition, we prove that recessive solutions are the ...
Došlá Zuzana +2 more
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Oscillatory and nonoscillatory solutions of neutral differential equations [PDF]
Annales Polonici Mathematici, 2000 Consider the neutral differential equation \[ {d^n\over dt^n} \bigl[x(t)+ \lambda x(t-\tau) \bigr]+f\biggl( t,x\bigl(g(t) \bigr)\biggr) =0 \] with \(\lambda>0\), \(\tau>0\), \(g\in C([t_0,\infty))\), \(\lim_{t\to \infty} g(t)= \infty\), \(f\in C([t_0,\infty)\times\mathbb{R})\) and \(|f(t,u) |\leq F(t, |u|)\) where \(F\) is a continuous and ...
Tanaka, Satoshi
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Asymptotic decay of nonoscillatory solutions of general nonlinear difference equations [PDF]
International Journal of Mathematics and Mathematical Sciences, 2001 The authors consider the mth order nonlinear difference equations of the form Dmyn+qnf(yσ(n))=ei, where m≥1, n∈ℕ={0,1,2,…}, ani>0 for i=1,2,…,m−1, anm≡1, D0yn=yn, Diyn=aniΔDi−1yn, i=1,2,…,m, σ(n)→∞ as n→∞, and f:ℝ→ℝ is continuous with uf(u)>0 for u≠0 ...
E. Thandapani +2 more
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Nonoscillatory solutions for system of neutral delay equation
Nonlinear Analysis: Theory, Methods & Applications, 2003 The authors consider the following system of neutral differential equations \[ {d\over dt} (x(t)+ px(t- \tau))+ Q(t) x(t-\sigma)= 0,\tag{1} \] where \(p\in\mathbb{R}\), \(x\in\mathbb{R}^n\) and \(\tau\in (0,\infty)\), \(\sigma\in [0,\infty)\), \(Q\) is a continuous \(n\times n\)-matrix on \([t_0,\infty)\).
El-Metwally, H. +2 more
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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 +3 more
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