Results 51 to 60 of about 203 (148)
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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On oscillatory behavior of two-dimensional time scale systems
Advances in Difference Equations, 2018 This paper deals with long-time behaviors of nonoscillatory solutions of a system of first-order dynamic equations on time scales. Some well-known fixed point theorems and double improper integrals are used to prove the main results.
Özkan Öztürk
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A nonoscillation theorem for Emden–Fowler equations
Journal of Mathematical Analysis and Applications, 2002 The author proves a nonoscillation theorem for the second-order Emden-Fowler equation \[ \quad y''+a(x)| y| ^{\gamma-1}y=0, \quad \gamma>0, \tag{E} \] where \(a(x)\) is positive and absolutely continuous on \((0,\infty)\). Let \(\psi(x)=x^{(\gamma+3)/2+\delta}\) where \(\delta\) is any positive number. The following theorem is proved: Let \(\gamma \not
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Complex oscillation and nonoscillation results
Transactions of the American Mathematical Society, 2019 Let \(\mathbb{R}\) be the ring of entire functions, \(f\in\mathbb{R}\) , and let \(\lambda(f)\) and \(\sigma(f)\) denote the exponent of convergence of the zeros of \(f\) and the order of growth of \(f\), respectively. The following questions on the oscillation theory of solutions of the linear differential equation \[ y''+A(z)y=0\quad(A(z)\in\mathbb{R}
Heittokangas, Janne +3 more
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Electronic Journal of Differential Equations, 2016 We investigate oscillatory properties of even-order half-linear differential equations and conditions for negativity of the associated energy functional.
Ondrej Dosly, Vojtech Ruzicka
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OSCILLATION PROPERTIES OF A CLASS OF SECOND ORDER NEUTRAL DIFFERENTIAL EQUATIONS WITH PIECEWISE CONSTANT ARGUMENTS [PDF]
Romanian Journal of Mathematics and Computer Science, 2015 In this work, we investigate the oscillation and nonoscillation of a class of second order neutral di erential equations with piecewise constant arguments of the form: ((r(t)(y(t) + p(t)y(t-1))')' + q(t)y([t-1]) = f(t); where [ ] denotes the greatest ...
A. K. TRIPATHY, R. R. MOHANTA
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AxiomsIn this paper, we address the study of the oscillatory properties of the solutions of a class of third-order delay differential equations. The primary objective of this study is to provide new relationships that can be employed to obtain criteria for ...
Asma Al-Jaser +3 more
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Local estimates for modified Riccati equation in theory of half-linear differential equation
Electronic Journal of Qualitative Theory of Differential Equations, 2012 In this paper we study the half-linear differential equation \begin{equation*} \bigl(r(t)\Phi_p(x')\bigr)'+c(t)\Phi_p(x)=0, \end{equation*} where $\Phi_p(x)=|x|^{p-2}x$, $p>1$. Using modified Riccati technique and suitable local estimates for terms
Simona Fišnarová, Robert Marik
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On Nonoscillation of Systems of Delay Equations
Funkcialaj Ekvacioj, 2011 The paper investigates nonnegativity of all entries of the fundamental matrix for the system of linear delay differential equations $\dot{X}$(t)+$\sum_{k=1}^m$ Ak(t)X(hk(t))=0 in the case when the non-diagonal entries of matrices Ak are nonpositive.
Berezansky, L. +2 more
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