On the distribution of zeros and asymptotic properties of the solutions of linear differential equations of the third order

1973 ◽  
Vol 4 (4) ◽  
pp. 307-314 ◽  
Author(s):  
Rahmi Ibrahim Ibrahim Abdel Karim
Keyword(s):  
Differential Equations ◽  
Asymptotic Properties ◽  
Linear Differential Equations ◽  
Distribution Of Zeros ◽  
Third Order ◽  
The Third ◽  
Linear Differential

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 Some Extensions of Pincherle's Polynomials

1920 ◽  
Vol 39 ◽  
pp. 21-24 ◽  
Author(s):  
Pierre Humbert
Keyword(s):  
Differential Equation ◽  
General Theory ◽  
Differential Equations ◽  
Second Order ◽  
Linear Differential Equations ◽  
Third Order ◽  
The Third ◽  
Hypergeometric Type ◽  
Linear Differential ◽  
Image Position

The polynomials which satisfy linear differential equations of the second order and of the hypergeometric type have been the object of extensive work, and very few properties of them remain now hidden; the student who seeks in that direction a subject for research is compelled to look, not after these functions themselves but after generalisations of them. Among these may be set in first place the polynomials connected with a differential equation of the third order and of the extended hypergeometric type, of which a general theory has been given by Goursat. The number of such polynomials of which properties have been studied in particular is rather small; in fact, Appell's polynomialsand Pincherle's polynomials, arising from the expansionsare, so far as I know, the only well-known ones. To show what can be done in these ways, I shall briefly give the definition and principal properties of some polynomials analogous to Pincherle's and of some allied functions.

scholarly journals The third order modular linear differential equations

2017 ◽  
Vol 485 ◽  
pp. 332-352 ◽  
Author(s):  
Masanobu Kaneko ◽  
Kiyokazu Nagatomo ◽  
Yuichi Sakai
Keyword(s):  
Differential Equations ◽  
Linear Differential Equations ◽  
Third Order ◽  
The Third ◽  
Linear Differential

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.

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