Asymptotic behavior of the solutions of the third order nonlinear differential equationsu‴±tσ u n =0u n =0

1975 ◽  
Vol 104 (1) ◽  
pp. 43-65 ◽  
Author(s):  
Paul A. Ohme
Keyword(s):  
Asymptotic Behavior ◽  
Third Order ◽  
The Third

scholarly journals On the asymptotic behavior of solutions of certain third-order nonlinear differential equations

2005 ◽  
Vol 2005 (1) ◽  
pp. 29-35 ◽  
Author(s):  
Cemil Tunç
Keyword(s):  
Differential Equation ◽  
Asymptotic Behavior ◽  
Differential Equations ◽  
Nonlinear Differential Equation ◽  
Nonlinear Differential Equations ◽  
Sufficient Conditions ◽  
Asymptotic Behavior Of Solutions ◽  
Third Order ◽  
The Third ◽  
All Solutions

We establish sufficient conditions under which all solutions of the third-order nonlinear differential equation x ⃛+ψ(x,x˙,x¨)x¨+f(x,x˙)=p(t,x,x˙,x¨) are bounded and converge to zero as t→∞.

scholarly journals Oscillatory and Asymptotic Behavior of Third Order Half-linear Neutral Dierential Equation with \Maxima"

2017 ◽  
Vol 13 (3) ◽  
pp. 7219-7229
Author(s):  
R Arul ◽  
A Ashok ◽  
G Ayyappan
Keyword(s):  
Asymptotic Behavior ◽  
Third Order ◽  
The Third ◽  
Positive Integers

In this paper we study the oscillation and asymptotic behavior of the third orderneutral dierential equation with \maxima" of the formwhere is the quotient of odd positive integers. Some examples are given toillustrate the main results.

scholarly journals On nonoscillatory solutions tending to zero of third-order nonlinear differential equations

2011 ◽  
Vol 48 (1) ◽  
pp. 135-143 ◽  
Author(s):  
Ivan Mojsej ◽  
Alena Tartal’ová
Keyword(s):  
Asymptotic Behavior ◽  
Differential Equations ◽  
Nonlinear Differential Equations ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Asymptotic Behavior Of Solutions ◽  
Third Order ◽  
Nonoscillatory Solutions ◽  
The Third ◽  
Necessary And Sufficient

Abstract The aim of this paper is to present some results concerning with the asymptotic behavior of solutions of nonlinear differential equations of the third-order with quasiderivatives. In particular, we state the necessary and sufficient conditions ensuring the existence of nonoscillatory solutions tending to zero as t → ∞.

scholarly journals Asymptotic behavior of third order delay difference equations with a negative middle term

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
S. H. Saker ◽  
S. Selvarangam ◽  
S. Geetha ◽  
E. Thandapani ◽  
J. Alzabut
Keyword(s):  
Asymptotic Behavior ◽  
Difference Equation ◽  
Sufficient Conditions ◽  
Delay Difference Equation ◽  
Third Order ◽  
Nonoscillatory Solutions ◽  
Middle Term ◽  
The Third ◽  
Delay Difference Equations ◽  
Delay Difference

AbstractIn this paper, we establish some sufficient conditions which ensure that the solutions of the third order delay difference equation with a negative middle term $$ \Delta \bigl(a_{n}\Delta (\Delta w_{n})^{\alpha } \bigr)-p_{n}(\Delta w_{n+1})^{ \alpha }-q_{n}h(w_{n-l})=0,\quad n\geq n_{0}, $$ Δ ( a n Δ ( Δ w n ) α ) − p n ( Δ w n + 1 ) α − q n h ( w n − l ) = 0 , n ≥ n 0 , are oscillatory. Moreover, we study the asymptotic behavior of the nonoscillatory solutions. Two illustrative examples are included for illustration.

scholarly journals Asymptotic Properties of Third-Order Delay Trinomial Differential Equations

2011 ◽  
Vol 2011 ◽  
pp. 1-10 ◽  
Author(s):  
J. Džurina ◽  
R. Komariková
Keyword(s):  
Differential Equation ◽  
Asymptotic Behavior ◽  
Differential Equations ◽  
Asymptotic Properties ◽  
Comparison Theorems ◽  
Asymptotic Behavior Of Solutions ◽  
Third Order ◽  
The Third

The aim of this paper is to study properties of the third-order delay trinomial differential equation((1/r(t))y′′(t))′+p(t)y′(t)+q(t)y(σ(t))=0, by transforming this equation onto the second-/third-order binomial differential equation. Using suitable comparison theorems, we establish new results on asymptotic behavior of solutions of the studied equations. Obtained criteria improve and generalize earlier ones.

scholarly journals Asymptotic Behavior of Solutions of the Third Order Nonlinear Mixed Type Neutral Differential Equations

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 485 ◽  
Author(s):  
Osama Moaaz ◽  
Dimplekumar Chalishajar ◽  
Omar Bazighifan
Keyword(s):  
Asymptotic Behavior ◽  
Differential Equations ◽  
Mixed Type ◽  
Asymptotic Properties ◽  
Asymptotic Behavior Of Solutions ◽  
Third Order ◽  
Neutral Differential Equations ◽  
The Third ◽  
Delayed Arguments ◽  
Advanced And Delayed Arguments

The objective of our paper is to study asymptotic properties of the class of third order neutral differential equations with advanced and delayed arguments. Our results supplement and improve some known results obtained in the literature. An illustrative example is provided.

Probe size and 5th-order aberration

1987 ◽  
Vol 45 ◽  
pp. 134-135 ◽  
Author(s):  
Zhifeng Shao
Keyword(s):  
Electron Probe ◽  
Spherical Aberration ◽  
Wave Length ◽  
Cylindrical Symmetry ◽  
Electron Wave ◽  
Third Order ◽  
The Third ◽  
Probe Radius ◽  
Small Probe ◽  
Probe Size

A small electron probe has many applications in many fields and in the case of the STEM, the probe size essentially determines the ultimate resolution. However, there are many difficulties in obtaining a very small probe.Spherical aberration is one of them and all existing probe forming systems have non-zero spherical aberration. The ultimate probe radius is given byδ = 0.43Csl/4ƛ3/4where ƛ is the electron wave length and it is apparent that δ decreases only slowly with decreasing Cs. Scherzer pointed out that the third order aberration coefficient always has the same sign regardless of the field distribution, provided only that the fields have cylindrical symmetry, are independent of time and no space charge is present. To overcome this problem, he proposed a corrector consisting of octupoles and quadrupoles.

Children’s Recall of Approximations to English

1973 ◽  
Vol 16 (2) ◽  
pp. 201-212 ◽  
Author(s):  
Elizabeth Carrow ◽  
Michael Mauldin
Keyword(s):  
Language Development ◽  
Fourth Order ◽  
Third Order ◽  
Memory Processes ◽  
The Third ◽  
General Index ◽  
General Linguistic

As a general index of language development, the recall of first through fourth order approximations to English was examined in four, five, six, and seven year olds and adults. Data suggested that recall improved with age, and increases in approximation to English were accompanied by increases in recall for six and seven year olds and adults. Recall improved for four and five year olds through the third order but declined at the fourth. The latter finding was attributed to deficits in semantic structures and memory processes in four and five year olds. The former finding was interpreted as an index of the development of general linguistic processes.

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