On the boundedness and periodicity of the solutions of a certain vector differential equation of third-order

1999 ◽  
Vol 20 (2) ◽  
pp. 163-170 ◽  
Author(s):  
Cemil Tunç
Keyword(s):  
Differential Equation ◽  
Third Order ◽  
Vector Differential Equation

scholarly journals Spherical curves and quadratic relationships for special functions

1985 ◽  
Vol 27 (1) ◽  
pp. 111-124
Author(s):  
Even Mehlum ◽  
Jet Wimp
Keyword(s):  
Differential Equation ◽  
Hypergeometric Functions ◽  
Bessel Functions ◽  
Special Functions ◽  
Position Vector ◽  
Third Order ◽  
Generalized Hypergeometric Functions ◽  
Transcendental Functions ◽  
Horn Functions ◽  
Vector Differential Equation

AbstractWe show that the position vector of any 3-space curve lying on a sphere satisfies a third-order linear (vector) differential equation whose coefficients involve a single arbitrary function A(s). By making various identifications of A(s), we are led to nonlinear identities for a number of higher transcendental functions: Bessel functions, Horn functions, generalized hypergeometric functions, etc. These can be considered natural geometrical generalizations of sin2t + cos2t = 1. We conclude with some applications to the theory of splines.

scholarly journals Convergence of Solutions to a Certain Vector Differential Equation of Third Order

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Cemil Tunç ◽  
Melek Gözen
Keyword(s):  
Differential Equation ◽  
Theoretical Analysis ◽  
Sufficient Conditions ◽  
Third Order ◽  
Convergence Of Solutions ◽  
Nonlinear Vector ◽  
Vector Differential Equation ◽  
Made In

We give some sufficient conditions to guarantee convergence of solutions to a nonlinear vector differential equation of third order. We prove a new result on the convergence of solutions. An example is given to illustrate the theoretical analysis made in this paper. Our result improves and generalizes some earlier results in the literature.

scholarly journals Position Vectors of Curves Generalizing General Helices and Slant Helices in Euclidean 3-Space

2021 ◽  
Vol 52 ◽  
Author(s):  
Malika Izid ◽  
Abderrazak El Haimi ◽  
Amina Ouazzani Chahdi
Keyword(s):  
Differential Equation ◽  
Parametric Representation ◽  
Position Vector ◽  
Third Order ◽  
The Third ◽  
Slant Helix ◽  
Vector Differential Equation ◽  
Standard Frame

Inthispaper,wegiveanewcharacterizationofak-slanthelixwhichisageneral- ization of general helix and slant helix. Thereafter, we construct a vector differential equation of the third order to determine the parametric representation of a k-slant helix according to standard frame in Euclidean 3-space. Finally, we apply this method to find the position vector of some examples of 2-slant helix by means of intrinsic equations.

Boundary-Value Problems for Third-Order Lipschitz Ordinary Differential Equations

2014 ◽  
Vol 58 (1) ◽  
pp. 183-197 ◽  
Author(s):  
John R. Graef ◽  
Johnny Henderson ◽  
Rodrica Luca ◽  
Yu Tian
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Boundary Value Problems ◽  
Order Differential Equation ◽  
Boundary Value ◽  
Point Boundary ◽  
Third Order ◽  
Optimal Length ◽  
The Third

AbstractFor the third-order differential equationy′″ = ƒ(t, y, y′, y″), where, questions involving ‘uniqueness implies uniqueness’, ‘uniqueness implies existence’ and ‘optimal length subintervals of (a, b) on which solutions are unique’ are studied for a class of two-point boundary-value problems.

Asymptotics for third-order nonlinear differential equations: Non-oscillatory and oscillatory cases

2021 ◽  
pp. 1-19
Author(s):  
Calogero Vetro ◽  
Dariusz Wardowski
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Order Differential Equation ◽  
Nonlinear Differential Equations ◽  
Oscillatory Behavior ◽  
Third Order ◽  
First Order ◽  
Third Order Differential Equation ◽  
Comparison Technique ◽  
First Order Differential Equations

We discuss a third-order differential equation, involving a general form of nonlinearity. We obtain results describing how suitable coefficient functions determine the asymptotic and (non-)oscillatory behavior of solutions. We use comparison technique with first-order differential equations together with the Kusano–Naito’s and Philos’ approaches.

scholarly journals Asymptotic Dichotomy in a Class of Third-Order Nonlinear Differential Equations with Impulses

2010 ◽  
Vol 2010 ◽  
pp. 1-20 ◽  
Author(s):  
Kun-Wen Wen ◽  
Gen-Qiang Wang ◽  
Sui Sun Cheng
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Nonlinear Differential Equation ◽  
Nonlinear Differential Equations ◽  
Functional Differential Equations ◽  
Higher Order ◽  
Third Order ◽  
Order Nonlinear Differential Equation ◽  
Functional Differential

Solutions of quite a few higher-order delay functional differential equations oscillate or converge to zero. In this paper, we obtain several such dichotomous criteria for a class of third-order nonlinear differential equation with impulses.

scholarly journals Existence and Lyapunov Stability of Positive Periodic Solutions for a Third-Order Neutral Differential Equation

2011 ◽  
Vol 2011 ◽  
pp. 1-28 ◽  
Author(s):  
Jingli Ren ◽  
Zhibo Cheng ◽  
Yueli Chen
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Periodic Solutions ◽  
Lyapunov Stability ◽  
Order Differential Equation ◽  
Sufficient Conditions ◽  
Neutral Differential Equation ◽  
Positive Periodic Solutions ◽  
Third Order

By applying Green's function of third-order differential equation and a fixed point theorem in cones, we obtain some sufficient conditions for existence, nonexistence, multiplicity, and Lyapunov stability of positive periodic solutions for a third-order neutral differential equation.

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