Results 21 to 30 of about 4,377 (209)
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 ...
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Asymptotic behavior of nonoscillatory solutions of higher-order integro-dynamic equations [PDF]
Opuscula Mathematica, 2014 In this paper, we establish some new criteria on the asymptotic behavior of nonoscillatory solutions of higher-order integro-dynamic equations on time scales.
Martin Bohner +2 more
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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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Unstable neutral differential equations involving the maximum function [PDF]
, 2005 A nonlinear differential equation involving the maximum function is studied. The existence and asymptotic behavior of nonoscillatory solutions are considered.
Guang Zhang, Malgorzata Migda
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Nonexistence of Unbounded Nonoscillatory Solutions of Partial Difference Equations
Journal of Mathematical Analysis and Applications, 1997 The authors develop criteria for the nonexistence of eventually positive (negative) and nondecreasing (nonincreasing) solutions of the partial difference equation \[ \nabla_m \nabla_n y(m,n)+ P\bigl(m,n,y (m+k, n+l)\bigr) =Q \bigl(m,n, y(m+k,n-l) \bigr) \] and \[ \nabla_m \nabla_n y(m,n)+ \sum^\tau_{i=1} P_i\bigl(m,n,y (m+k_i, n+l_i)\bigr)= \sum^\tau_ ...
Wong, P.J.Y., Agarwal, R.P.
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Existence of Nonoscillatory Solutions of First‐Order Neutral Differential Equations [PDF]
Abstract and Applied Analysis, 2011 This paper contains some sufficient conditions for the existence of positive solutions which are bounded below and above by positive functions for the first‐order nonlinear neutral differential equations.
Dorociaková, Božena +2 more
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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 ...
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Asymptotically polynomial solutions of difference equations of neutral type
, 2014 Asymptotic properties of solutions of difference equation of the form \[ \Delta^m(x_n+u_nx_{n+k})=a_nf(n,x_{\sigma(n)})+b_n \] are studied. We give sufficient conditions under which all solutions, or all solutions with polynomial growth, or all ...
Migda, Janusz
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Nonoscillatory solutions of neutral differential equations
Hiroshima Mathematical Journal, 1990 The paper deals with the neutral ODE \((*)\quad (d^ n/dt^ n)(x(t)- h(t)x(s(t)))+kp(t)f(x(g(t)))=0,\) \(n\geq 2\), \(k^ 2=1\), \(s(t)0\) for \(u\neq 0\), g(t)\(\to \infty\), \(t\to \infty\). A systematic study of the structure of all nonoscillatory solutions of the equation (*) is given.
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Comparison theorems for fourth order differential equations
International Journal of Mathematics and Mathematical Sciences, 1986 This paper establishes an apparently overlooked relationship between the pair of fourth order linear equations yiv−p(x)y=0 and yiv+p(x)y=0, where p is a positive, continuous function defined on [0,∞).
Garret J. Etgen, Willie E. Taylor
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