Oscillation of third order trinomial delay differential equations

Baculíková, Blanka; Džurina, Jozef; Rogovchenko, Yuri V.

doi:10.1016/j.amc.2011.12.049

Cited by 25 publications

(12 citation statements)

References 24 publications

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“…is often applied, see [2], [4], [5] or [11]. Such a method was also used to the discrete counterpart of equation (4).…”

Section: Introductionmentioning

confidence: 99%

“…A criteria which ensures that all nonoscillatory solutions of (5) tend to zero was established. In [12], criteria for oscillation of bounded solutions and sufficient conditions for the existence of certain types of nonoscillatory solutions of nonlinear equation of type (5), are obtained. Here also the transformation to a binomial difference equation with quasidifferences was used.…”

Section: Introductionmentioning

confidence: 99%

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Asymptotic properties of solutions of third order difference equations

Migda

Nockowska-Rosiak

2020

APPL ANAL DISCRETE M

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We consider the difference equation of the form ∆(rn∆(pn∆xn)) = anf (x σ(n)) + bn. We present sufficient conditions under which, for a given solution y of the equation ∆(rn∆(pn∆yn)) = 0, there exists a solution x of the nonlinear equation with the asymptotic behavior xn = yn + zn, where z is a sequence convergent to zero. Our approach allows us to control the degree of approximation, i.e., the rate of convergence of the sequence z. We examine two types of approximation: harmonic approximation when zn = o(n s), s ≤ 0, and geometric approximation when zn = o(µ n), µ ∈ (0, 1).

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“…is often applied, see [2], [4], [5] or [11]. Such a method was also used to the discrete counterpart of equation (4).…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Asymptotic properties of solutions of third order difference equations

Migda

Nockowska-Rosiak

2020

APPL ANAL DISCRETE M

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“…Being aware of numerous indications of the practical importance of third-order differential equations as well as a number of mathematical problems involved [2], the area of the qualitative theory for such equations has attracted a large portion of research interest in the last three decades. The asymptotic properties of equations of type (1) with p ≡ 0 were extensively investigated in the literature, see, e.g., [3][4][5][6][7][8][9][10][11][12][13][14] and the references cited therein. Most of the papers have been devoted to the examination of so-called canonical equations, where conditions opposite to (2) hold, namely,…”

Section: Introductionmentioning

confidence: 99%

Oscillatory Properties of Third-Order Neutral Delay Differential Equations with Noncanonical Operators

2019

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In the paper, we study the oscillatory and asymptotic properties of solutions to a class of third-order linear neutral delay differential equations with noncanonical operators. Via the application of comparison principles with associated first and second-order delay differential inequalities, we offer new criteria for the oscillation of all solutions to a given differential equation. Our technique essentially simplifies the process of investigation and reduces the number of conditions required in previously known results. The strength of the newly obtained results is illustrated on the Euler type equations.

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“…This approach has been used by many authors, see e.g. [5], [8], [9], [10], [21]. If (2) is nonoscillatory, then the result [3], Theorem 2.2 with n = 3 reads as follows.…”

Section: Introductionmentioning

confidence: 99%

“…Special attention has been paid to the third order equations with quasi-derivatives, see e.g. [11], [10], with damping term [5], [9], [7] or with deviating argument [1] and the references therein.…”

Section: Introductionmentioning

confidence: 99%