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Asymptotic behavior of even-order noncanonical neutral differential equations

Moaaz Osama, Muhib Ali, Abdeljawad Thabet, Santra Shyam S., Anis Mona

Demonstratio Mathematica

2022

Vol. 55, nr 1

28--39

In this article, we study the asymptotic behavior of even-order neutral delay differential equation (a⋅(u+ρ⋅u∘τ)(n−1))′(ℓ)+h(ℓ)u(g(ℓ))=0,ℓ≥ℓ0, where n≥4, and in noncanonical case, that is, ∞∫a−1(s)ds<∞. To the best of our knowledge, most of the previous studies were concerned only with the study of n-order neutral equations in canonical case. By using comparison principle and Riccati transformation technique, we obtain new criteria which ensure that every solution of the studied equation is either oscillatory or converges to zero. Examples are presented to illustrate our new results.

Oscillatory behavior of even-order nonlinear differential equations with a sublinear neutral term

Graef John R., Grace Said R., Tunc Ercan

Opuscula Mathematica

2019

Vol. 39, no. 1

39--47

The authors present a new technique for the linearization of even-order nonlinear differential equations with a sublinear neutral term. They establish some new oscillation criteria via comparison with higher-order linear delay differential inequalities as well as with first-order linear delay differential equations whose oscillatory characters are known. Examples are provided to illustrate the theorems.

About oscillatory behavior of solutions when passing from difference to differential equations

Komashynska I., Ateiwi A.

Demonstratio Mathematica

2005

Vol. 38, nr 4

867--874

We study a second order difference equations. We obtain conditions of preservation of solutions when passmg from difference to differential equations.