Results 61 to 70 of about 186 (128)

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, Ishizaki, Katsuya, Laine, Ilpo, Tohge, Kazuya   +3 more
openaire   +1 more source

Nonoscillation criteria and energy functional for even-order half-linear two-term differential equations

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
doaj  

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 dierential 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
doaj  

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
doaj   +1 more source

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
openaire   +1 more source

Investigation of the Oscillatory Behavior of the Solutions of a Class of Third-Order Delay Differential Equations with Several Terms

Axioms
In 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, Insaf F. Ben Saoud, Higinio Ramos, Belgees Qaraad   +3 more
doaj   +1 more source

Qualitative properties of a third-order differential equation with a piecewise constant argument

Electronic Journal of Differential Equations, 2017
We consider a third order differential equation with piecewise constant argument and investigate oscillation, nonoscillation and periodicity properties of its solutions.
Huseyin Bereketoglu, Mehtap Lafci, Gizem S. Oztepe   +2 more
doaj  

Nonoscillation in a delay-logistic equation [PDF]

Quarterly of Applied Mathematics, 1985
Consider the equation \(x'(t)=x(t)(b-\sum^{n}_{j=1}a_ jx(t-\tau_ j),\) \(a_ j\), b, \(\tau_ j\) positive constants, with the initial function \(\phi\) (s)\(\geq 0\), \(\phi (0)>0\). Assume \((\sum^{n}_{j=1}a_ j)x^*\tau \leq 1/e,\) \(x^*=b/(\sum^{n}_{j=1}a_ j)\), \(\tau =\max \tau_ j\). Then there exists a solution such that \(x(t)-x^*\) has no zeros on
openaire   +2 more sources

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
doaj   +1 more source

On the Nonoscillation of Second-Order Neutral Delay Differential Equation with Forcing Term

Discrete Dynamics in Nature and Society, 2008
This paper is concerned with nonoscillation of second-order neutral delay differential equation with forcing term. By using contraction mapping principle, some sufficient conditions for the existence of nonoscillatory solution are established.
Jin-Zhu Zhang, Zhen Jin, Tie-Xiong Su, Jian-Jun Wang, Zhi-Yu Zhang, Ju-Rang Yan   +5 more
doaj   +1 more source