Results 31 to 40 of about 7,785,042 (211)
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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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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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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Oscillation criteria for third order nonlinear delay differential equations with damping [PDF]
Opuscula Mathematica, 2015 This note is concerned with the oscillation of third order nonlinear delay differential equations of the form \[\label{*} \left( r_{2}(t)\left( r_{1}(t)y^{\prime}(t)\right)^{\prime}\right)^{\prime}+p(t)y^{\prime}(t)+q(t)f(y(g(t)))=0.\tag{\(\ast\)}\] In ...
Said R. Grace
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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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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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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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On the Asymptotic Behavior of Nonoscillatory Solutions of Certain Fractional Differential Equations
Opuscula Mathematica, 2018 We present the conditions under which every nonoscillator solution x(t) of the forced fractional differential equation $$\begin{aligned} ^{\mathrm{C}}D_{\mathrm{c}}^{\alpha } y ( t ) = e ( t ) +f ( {t, x ( t )} ), c > 1,\alpha \in ( {0,1} ), \quad ...
J. Graef, S. Grace, E. Tunç
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Journal of Al-Qadisiyah for Computer Science and Mathematics, 2020 In this paper, authors obtained sufficient conditions to ensure that every bounded solution of nth order nonlinear neutral differential system oscillates or nonoscillatory converges to zero as t→∞, some examples were given to explain the results obtained.
Noor Abdulameer Abdulkareem +2 more
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Nonoscillatory solutions of higher order delay equations
Journal of Mathematical Analysis and Applications, 1980 where f is a continuous real valued function for f > 0 and x E R such that f(t, x) is nondecreasing in x for fixed t, and xf(t, x) > 0 if x # 0. The delay function g(t) is continuous and satisfies g(t) to in that it satisfies for r>, t, x(t)x”‘(t) > 0 for i = 0, l,..., I, and (-1)“’ ‘x(t)x”‘(t) < 0, i = 1 + 1, I + 2 ,..., n.
Foster, K.E, Grimmer, R.C
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