Results 51 to 60 of about 186 (128)
A remark on the linearization technique in half-linear oscillation theory [PDF]
Opuscula Mathematica, 2006 We show that oscillatory properties of the half-linear second order differential equation \[(r(t)\Phi(x'))'+c(t)\Phi(x)=0,\qquad\Phi(x)=|x|^{p-2}x,\quad p\gt 1,\] can be investigated via oscillatory properties of a certain associated second order linear ...
Ondřej Došlý
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Nonoscillation and disconjugacy in the complex domain [PDF]
Transactions of the American Mathematical Society, 1956 where p(z) is a function analytic in a region R of the complex plane. E. Hille [3; 4] was the first to make a systematic study of the distribution of the zeros of solutions of (0.1). His approach consisted of selecting a particular zero z=a of a particular solution w(z) of (0.1), and then constructing a zero-free region about z =a, i.e., a region about
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Nonoscillation of third order retarded equations [PDF]
Bulletin of the Australian Mathematical Society, 1974 The third order delay equationy‴(t) + a(t)yτ(t) = 0is studied for its nonoscillatory nature under the general condition in which a(t) has been allowed to oscillate. It is shown by way of a differential inequality that if g(t) is a thrice differentiable and eventually positive function theng‴(t) + t2|a(t)|g(t) ≤ 0is sufficient for this equation to have ...
Singh, Bhagat, Dahiya, R. S.
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New nonoscillation criteria for delay differential equations
Journal of Mathematical Analysis and Applications, 2004 The authors consider first-order delay differential equations of the form \[ x'(t)+p(t)x(\tau(t))=0,\quad t\geq t_0, \] where \(p, \tau\in C([t_0, \infty), [0, \infty)), \tau(t)\) is nondecreasing, \(\tau(t)
Shen, Jianhua, Tang, Xianhua
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Oscillation and Nonoscillation for Neutral Differential Equations
Journal of Mathematical Analysis and Applications, 1993 A class of neutral differential equations is investigated. The existence of nonoscillatory positive solutions is proved. Sufficient conditions for the existence of oscillatory solutions of this problem are given.
Zhang, B.G., Yu, J.S.
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Advanced impulsive differential equations with piecewise constant arguments
Mathematical Modelling and Analysis, 2010 We prove the existence and uniqueness of the solutions of a class of first order nonhomogeneous advanced impulsive differential equations with piecewise constant arguments.
Hüseyin Bereketoglu +2 more
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Nonoscillation Theorems for a Nonlinear Differential Equation [PDF]
Proceedings of the American Mathematical Society, 1970 This paper is concerned with the problem of specifying growth conditions on the positive function q ( t ) q(t) which imply that all solutions of the nonlinear second order ordinary differential equation y + q ( t ) | y
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Nonoscillation in nonlinear difference equations
Computers & Mathematics with Applications, 1994 The authors establish some necessary conditions on the nonoscillation of the nonlinear difference equation \(\Delta \psi (\Delta x_{k - 1}) + a_ k \psi (x_ k) = 0\), \(k = 1,2, \dots\), where \(\psi : \mathbb{R} \to \mathbb{R}\) is defined by \(\psi (s) = | s |^{p - 2} s\) with \(p > 1\) a fixed real number, and \(\{a_ k\}^ \infty_ 1\) is a nonnegative
Li, Horng Jaan, Yeh, Cheh Chih
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Nonoscillation of First-Order Dynamic Equations with Several Delays
Advances in Difference Equations, 2010 For dynamic equations on time scales with positive variable coefficients and several delays, we prove that nonoscillation is equivalent to the existence of a positive solution for the generalized characteristic inequality and to the positivity of the ...
Karpuz Başak, Braverman Elena
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Electronic Journal of Differential Equations, 2013 In this article, we investigate the oscillation and nonoscillation of second order nonlinear neutral dynamic equations with retarded and advanced arguments by means of the theory of upper and lower solutions for related dynamic equations along with ...
Xun-Huan Deng, Qi-Ru Wang
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