Instability of solution for the third order linear differential equation with varied coefficient

1988 ◽  
Vol 9 (10) ◽  
pp. 969-984 ◽  
Author(s):  
Liao Zong-huang ◽  
Lu De-yuan
Keyword(s):  
Differential Equation ◽  
Linear Differential Equation ◽  
Order Linear Differential Equation ◽  
Third Order ◽  
Order Linear ◽  
The Third ◽  
Linear Differential

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.

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 THE TRANSFORMATION OF THE LINEAR DIFFERENTIAL EQUATION INTO A SYSTEM OF THE FIRST ORDER EQUATIONS

2019 ◽  
pp. 71-75
Author(s):  
M.I. Ayzatsky
Keyword(s):  
Differential Equation ◽  
Linear Differential Equation ◽  
Linear Equation ◽  
Second Order ◽  
Dimensional System ◽  
Third Order ◽  
Order Linear ◽  
First Order ◽  
The Third ◽  
Linear Differential

The generalization of the transformation of the linear differential equation into a system of the first order equations is presented. The proposed transformation gives possibility to get new forms of the N-dimensional system of first order equations that can be useful for analysis of the solutions of the N-th-order differential equations. In particular, for the third-order linear equation the nonlinear second-order equation that plays the same role as the Riccati equation for second-order linear equation is obtained.

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