scholarly journals An explicit characterization of spherical curves according to bishop frame and an approximately solution

2019 ◽  
Vol 23 (Suppl. 1) ◽  
pp. 361-370
Author(s):  
Pınar Balki-Okullu ◽  
Huseyin Kocayigit ◽  
Tuba Agirman-Aydin
Keyword(s):  
Differential Equation ◽  
Linear Differential Equation ◽  
Series Solution ◽  
Solution Method ◽  
Position Vector ◽  
Order Linear Differential Equation ◽  
Third Order ◽  
Bishop Frame ◽  
Linear Differential

In this paper, spherical curves are studied by using Bishop frame. First, the differential equation characterizing the spherical curves is given. Then, we exhibit that the position vector of a curve which is lying on a sphere satisfies a third-order linear differential equation. Then we solve this linear differential equation by using Bernstein series solution method.

scholarly journals Differential representation of the Lorentzian spherical timelike curves by using bishop frame

2019 ◽  
Vol 23 (Suppl. 6) ◽  
pp. 2037-2043
Author(s):  
Okullu Balki ◽  
Huseyin Kocayigit
Keyword(s):  
Differential Equation ◽  
Linear Differential Equation ◽  
Timelike Curve ◽  
Position Vector ◽  
Order Linear Differential Equation ◽  
Third Order ◽  
Order Linear ◽  
Bishop Frame ◽  
Lorentzian Sphere ◽  
Linear Differential

In this study, we will give the differential representation of the Lorentzian spherical timelike curves according to Bishop frame and we obtain a third-order linear differential equation which represents the position vector of a timelike curve lying on a Lorentzian sphere.

scholarly journals On spectra of upper Sergeev frequencies of linear differential equations

2019 ◽  
pp. 28-32
Author(s):  
Aliaksei S. Vaidzelevich
Keyword(s):  
Differential Equation ◽  
Positive Integer ◽  
Linear Differential Equation ◽  
Fourth Order ◽  
Real Line ◽  
Half Line ◽  
Integer Number ◽  
Order Linear Differential Equation ◽  
Third Order ◽  
Linear Differential

It is known that the spectra (ranges) of upper and lower Sergeev frequencies of zeros, signs, and roots of a linear differential equation of order greater than two with continuous coefficients belong to the class of Suslin sets on the nonnegative half-line of the extended real line. Moreover, for the spectra of upper frequencies of third-order equations this result was inverted under the assumption that the spectra contain zero. In the present paper we obtain an inversion of the above statement for equations of the fourth order and higher. Namely, for an arbitrary zero-containing Suslin subset S on the non-negative half-line of the extended real line and a positive integer number n greater than three a n order linear differential equation is constructed, which spectra of the upper Sergeev frequencies of zeros, signs, and roots coincide with the set S.

Disconjugacy Conditions for the Third Order Linear Differential Equation

1969 ◽  
Vol 12 (5) ◽  
pp. 603-613 ◽  
Author(s):  
Lynn Erbe
Keyword(s):  
Differential Equation ◽  
Linear Differential Equation ◽  
Sufficient Conditions ◽  
Order Linear Differential Equation ◽  
Third Order ◽  
Order Linear ◽  
The Third ◽  
Counting Multiplicity ◽  
Linear Differential ◽  
Image Position

An nth order homogeneous linear differential equation is said to be disconjugate on the interval I of the real line in case no non-trivial solution of the equation has more than n - 1 zeros (counting multiplicity) on I. It is the purpose of this paper to establish several necessary and sufficient conditions for disconjugacy of the third order linear differential equation(1.1)where pi(t) is continuous on the compact interval [a, b], i = 0, 1, 2.

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