Results 21 to 30 of about 4,284 (195)
Remarks on the existence of nonoscillatory solutions of half-linear ordinary differential equations, I [PDF]
Opuscula Mathematica, 2021 We consider the half-linear differential equation of the form \[(p(t)|x'|^{\alpha}\mathrm{sgn} x')' + q(t)|x|^{\alpha}\mathrm{sgn} x = 0, \quad t\geq t_{0},\] under the assumption \(\int_{t_{0}}^{\infty}p(s)^{-1/\alpha}ds =\infty\). It is shown that if a
Manabu Naito
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Oscillation of Nonlinear Differential Equations with Advanced Arguments
مجلة بغداد للعلوم, 2008 This paper is concerned with the oscillation of all solutions of the n-th order delay differential equation . The necessary and sufficient conditions for oscillatory solutions are obtained and other conditions for nonoscillatory solution to converge ...
Baghdad Science Journal
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Oscillation of deviating differential equations [PDF]
Mathematica Bohemica, 2020 Consider the first-order linear delay (advanced) differential equation x'(t)+p(t)x( \tau(t)) =0\quad(x'(t)-q(t)x(\sigma(t)) =0),\quad t\geq t_0, where $p$ $(q)$ is a continuous function of nonnegative real numbers and the argument $\tau(t)$ $(\sigma(
George E. Chatzarakis
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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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Principal solution of half-linear differential equation: Limit and integral characterization
Electronic Journal of Qualitative Theory of Differential Equations, 2008 We investigate integral and limit characterizations of the principal solution of the nonoscillatory half-linear differential equation $$ (r(t)\Phi(x'))'+c(t)\Phi(x)=0,\quad \Phi(x)=|x|^{p-2},\ p>1 $$.
Zuzana Dosla, Ondrej Dosly
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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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Oscillation and non-oscillation of some neutral differential equations of odd order
International Journal of Mathematics and Mathematical Sciences, 1992 An existence criterion for nonoscillatory solution for an odd order neutral differential equation is provided. Some sufficient conditions are also given for the oscillation of solutions of some nth order equations with nonlinearity in the neutral term.
B. S. Lalli, B. G. Zhang
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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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Oscillations of advanced difference equations with variable arguments
Electronic Journal of Qualitative Theory of Differential Equations, 2012 Consider the first-order advanced difference equation of the form \begin{equation*} \nabla x(n)-p(n)x(\mu (n))=0\text{, }\ n\geq 1\, [\Delta x(n)-p(n)x(\nu (n))=0, n\geq 0], \end{equation*} where $\nabla $ denotes the backward difference operator ...
George Chatzarakis, Ioannis Stavroulakis
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