Displaying similar documents to “Necessary and sufficient conditions for oscillations of delay partial difference equations”

Boundedness of Third-order Delay Differential Equations in which is not necessarily Differentiable

Mathew O. Omeike (2015)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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In this paper we study the boundedness of solutions of some third-order delay differential equation in which is not necessarily differentiable but satisfy a Routh–Hurwitz condition in a closed interval .

Oscillation criteria for two dimensional linear neutral delay difference systems

Arun Kumar Tripathy (2023)

Mathematica Bohemica

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In this work, necessary and sufficient conditions for the oscillation of solutions of 2-dimensional linear neutral delay difference systems of the form are established, where , , are integers and , , , , are sequences of real numbers.

On oscillation of solutions of forced nonlinear neutral differential equations of higher order II

N. Parhi, R. N. Rath (2003)

Annales Polonici Mathematici

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Sufficient conditions are obtained so that every solution of where n ≥ 2, p,f ∈ C([0,∞),ℝ), Q ∈ C([0,∞),[0,∞)), G ∈ C(ℝ,ℝ), τ > 0 and σ ≥ 0, oscillates or tends to zero as . Various ranges of p(t) are considered. In order to accommodate sublinear cases, it is assumed that . Through examples it is shown that if the condition on Q is weakened, then there are sublinear equations whose solutions tend to ±∞ as t → ∞.

Oscillatory behavior of higher order neutral differential equation with multiple functional delays under derivative operator

R.N. Rath, K.C. Panda, S.K. Rath (2022)

Archivum Mathematicum

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In this article, we obtain sufficient conditions so that every solution of neutral delay differential equation oscillates or tends to zero as , where, is any positive integer, ,  and are bounded for each . Further, , , , , , and . The functional delays , and and all of them approach as . The results hold when and . This article extends, generalizes and improves some recent results, and further answers some unanswered questions from the literature. ...

Necessary and sufficient conditions for oscillation of second-order differential equations with nonpositive neutral coefficients

Arun K. Tripathy, Shyam S. Santra (2021)

Mathematica Bohemica

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In this work, we present necessary and sufficient conditions for oscillation of all solutions of a second-order functional differential equation of type where . Under the assumption , we consider two cases when and . Our main tool is Lebesgue’s dominated convergence theorem. Finally, we provide examples illustrating our results and state an open problem.

Solutions of an advance-delay differential equation and their asymptotic behaviour

Gabriela Vážanová (2023)

Archivum Mathematicum

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The paper considers a scalar differential equation of an advance-delay type where constants , , and are positive, and and are arbitrary. The behavior of its solutions for is analyzed provided that the transcendental equation has a positive real root. An exponential-type function approximating the solution is searched for to be used in proving the existence of a semi-global solution. Moreover, the lower and upper estimates are given for such a solution.

Delay-dependent stability conditions for fundamental characteristic functions

Hideaki Matsunaga (2023)

Archivum Mathematicum

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This paper is devoted to the investigation on the stability for two characteristic functions and , where and are real numbers and . The obtained theorems describe the explicit stability dependence on the changing delay . Our results are applied to some special cases of a linear differential system with delay in the diagonal terms and delay-dependent stability conditions are obtained.

Oscillation properties for a scalar linear difference equation of mixed type

Leonid Berezansky, Sandra Pinelas (2016)

Mathematica Bohemica

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The aim of this work is to study oscillation properties for a scalar linear difference equation of mixed type where is the difference operator and are sequences of real numbers for , and , . We obtain sufficient conditions for the existence of oscillatory and nonoscillatory solutions. Some asymptotic properties are introduced.

Global behavior of the difference equation

Raafat Abo-Zeid (2015)

Archivum Mathematicum

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In this paper, we introduce an explicit formula and discuss the global behavior of solutions of the difference equation where are positive real numbers and the initial conditions , , , are real numbers.