scholarly journals Dirichlet problem for a second-order ordinary differential equation with a distributed differentiation operator

2021 ◽  
Vol 21 (4) ◽  
pp. 37-44
Author(s):  
B.I. Efendiev ◽  
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Dirichlet Problem ◽  
Function Method ◽  
Order Differential Equation ◽  
Variable Coefficients ◽  
Differentiation Operator ◽  
Second Order ◽  
Order Ordinary Differential Equation ◽  
Second Order Differential Equation

For an ordinary second-order differential equation with an operator of continuously distributed differentiation with variable coefficients, a solution to the Dirichlet problem is constructed using the Green’s function method.

Cauchy problem for second-order ordinary differential equation with continuously distributed differentiation operator

2020 ◽  
Vol 20 (1) ◽  
pp. 15-20
Author(s):  
B.I. Efendiev ◽  
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Cauchy Problem ◽  
Fundamental Solution ◽  
Order Differential Equation ◽  
Differentiation Operator ◽  
Second Order ◽  
Order Ordinary Differential Equation ◽  
Second Order Differential Equation ◽  
The Cauchy Problem

In this paper, we construct the fundamental solution for ordinary second-order differential equation with continuously distributed differentiation operator. With the help of fundamental solution the solution of the Cauchy problem is written out.

scholarly journals Bounded Solutions of the Second Order Differential Equation x ?+f(x) x ?+g(x)=u(t)

2015 ◽  
Vol 12 (4) ◽  
pp. 822-825
Author(s):  
Baghdad Science Journal
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Order Differential Equation ◽  
Second Order ◽  
Bounded Solutions ◽  
Order Ordinary Differential Equation ◽  
Second Order Differential Equation ◽  
Derivatives Of

In this paper we prove the boundedness of the solutions and their derivatives of the second order ordinary differential equation x ?+f(x) x ?+g(x)=u(t), under certain conditions on f,g and u. Our results are generalization of those given in [1].

scholarly journals Generalized multitime expansions for equations with slowly varying coefficients

1984 ◽  
Vol 7 (1) ◽  
pp. 151-158
Author(s):  
L. E. Levine ◽  
W. C. Obi
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Differential Equations ◽  
Small Parameter ◽  
Time Scales ◽  
Constant Coefficient ◽  
Variable Coefficients ◽  
Second Order ◽  
Order Ordinary Differential Equation ◽  
Varying Coefficients

The successive terms in a uniformly valid multitime expansion of the solutions of constant coefficient differential equations containing a small parameterϵmay be obtained without resorting to secularity conditions if the time scalesti=ϵit(i=0,1,…)are used. Similar results have been achieved in some cases for equations with variable coefficients by using nonlinear time scales generated from the equations themselves. This paper extends the latter approach to the general second order ordinary differential equation with slowly varying coefficients and examines the restrictions imposed by the method.

The Existence of Continuable Solutions of a Second Order Differential Equation

1977 ◽  
Vol 29 (3) ◽  
pp. 472-479 ◽  
Author(s):  
G. J. Butler
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Real Line ◽  
Order Differential Equation ◽  
Nonlinear Ordinary Differential Equation ◽  
Second Order ◽  
The Real ◽  
Second Order Differential Equation ◽  
Image Position ◽  
Sign Restriction

A much-studied equation in recent years has been the second order nonlinear ordinary differential equationwhere q and f are continuous on the real line and, in addition, f is monotone increasing with yf(y) > 0 for y ≠ 0. Although the original interest in (1) lay largely with the case that q﹛t) ≧ 0 for all large values of t, a number of papers have recently appeared in which this sign restriction is removed.

Sign in / Sign up

Export Citation Format

Share Document