scholarly journals Distributions of Zeros of Solutions for Third-Order Differential Equations with Variable Coefficients

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Samir H. Saker ◽  
Mohammed A. Arahet
Keyword(s):  
Differential Equations ◽  
Lower Bounds ◽  
Variable Coefficients ◽  
Linear Differential Equations ◽  
Third Order ◽  
Order Linear ◽  
The Third ◽  
Hardy's Inequality ◽  
Zeros Of Solutions ◽  
Linear Differential

For the third-order linear differential equations of the formr(t)x′′(t)′+p(t)x′(t)+q(t)x(t)=0, we will establish lower bounds for the distance between zeros of a solution and/or its derivatives. The main results will be proved by making use of Hardy’s inequality and some generalizations of Opial and Wirtinger type inequalities.

scholarly journals The distribution of zeros of solutions for a class of third order differential equation

2021 ◽  
Vol 40 (5) ◽  
pp. 1301-1321
Author(s):  
Clemente Cesarano ◽  
Mohammed A. Arahet ◽  
Tareq M. Al-Shami
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Lower Bounds ◽  
Order Differential Equation ◽  
Linear Differential Equations ◽  
Distribution Of Zeros ◽  
Third Order ◽  
Order Linear ◽  
Zeros Of Solutions ◽  
Linear Differential

For third order linear differential equations of the form r(t)x'(t)''+ p(t)x'(t) + q(t)x(t) = 0; we will establish lower bounds for the distance between zeros of a solution and/or its derivatives. The main results will be proved by making use of Hardyís inequality, some generalizations of Opialís inequality and Boydís inequality.

scholarly journals Comparison theorems of Hille-Wintner type for third order linear differential equations

1980 ◽  
Vol 21 (2) ◽  
pp. 175-188 ◽  
Author(s):  
L. Erbe
Keyword(s):  
Differential Equations ◽  
Linear Equation ◽  
Linear Equations ◽  
Second Order ◽  
Linear Differential Equations ◽  
Comparison Theorems ◽  
Third Order ◽  
Order Linear ◽  
The Third ◽  
Linear Differential

Integral comparison theorems of Hille-Wintner type of second order linear equations are shown to be valid for the third order linear equation y‴ + q(t)y = 0.

scholarly journals On non-homogeneous canonical third-order linear differential equations

1994 ◽  
Vol 57 (2) ◽  
pp. 138-148 ◽  
Author(s):  
N. Parhi
Keyword(s):  
Differential Equations ◽  
Linear Equations ◽  
Sufficient Conditions ◽  
Linear Differential Equations ◽  
Third Order ◽  
Order Linear ◽  
Non Linear ◽  
Linear Differential ◽  
Non Linear Equations

AbstractIn this paper sufficient conditions have been obtained for non-oscillation of non-homogeneous canonical linear differential equations of third order. Some of these results have been extended to non-linear equations.

scholarly journals Hyers-Ulam Stability of the First-Order Matrix Differential Equations

2015 ◽  
Vol 2015 ◽  
pp. 1-7
Author(s):  
Soon-Mo Jung
Keyword(s):  
Differential Equations ◽  
Variable Coefficients ◽  
Linear Differential Equations ◽  
Ulam Stability ◽  
Order Linear ◽  
First Order ◽  
Matrix Differential Equations ◽  
Homogeneous Matrix ◽  
Linear Differential ◽  
Matrix Differential

We prove the generalized Hyers-Ulam stability of the first-order linear homogeneous matrix differential equationsy→'(t)=A(t)y→(t). Moreover, we apply this result to prove the generalized Hyers-Ulam stability of thenth order linear differential equations with variable coefficients.

Third Order Linear Differential Equations

1988 ◽  
Vol 72 (459) ◽  
pp. 68
Author(s):  
R. L. E. Schwarzenberger ◽  
M. Gregus
Keyword(s):  
Differential Equations ◽  
Linear Differential Equations ◽  
Third Order ◽  
Order Linear ◽  
Linear Differential
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