scholarly journals Hyers-Ulam Stability of Nonhomogeneous Linear Differential Equations of Second Order

2009 ◽  
Vol 2009 ◽  
pp. 1-7 ◽  
Author(s):  
Yongjin Li ◽  
Yan Shen
Keyword(s):  
Differential Equation ◽  
Exact Solution ◽  
Approximate Solution ◽  
Differential Equations ◽  
Second Order ◽  
Linear Differential Equations ◽  
Ulam Stability ◽  
Linear Differential ◽  
The Stability

The aim of this paper is to prove the stability in the sense of Hyers-Ulam of differential equation of second ordery′′+p(x)y′+q(x)y+r(x)=0. That is, iffis an approximate solution of the equationy′′+p(x)y′+q(x)y+r(x)=0, then there exists an exact solution of the equation near tof.

scholarly journals Aboodh transform and the stability of second order linear differential equations

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Ramdoss Murali ◽  
Arumugam Ponmana Selvan ◽  
Choonkil Park ◽  
Jung Rye Lee
Keyword(s):  
Differential Equations ◽  
Integral Transform ◽  
Second Order ◽  
Linear Differential Equations ◽  
Ulam Stability ◽  
Order Linear ◽  
Linear Differential ◽  
The Stability ◽  
Rassias Stability

AbstractIn this paper, we introduce a new integral transform, namely Aboodh transform, and we apply the transform to investigate the Hyers–Ulam stability, Hyers–Ulam–Rassias stability, Mittag-Leffler–Hyers–Ulam stability, and Mittag-Leffler–Hyers–Ulam–Rassias stability of second order linear differential equations.

scholarly journals Generalized Hyers-Ulam Stability of the Second-Order Linear Differential Equations

2011 ◽  
Vol 2011 ◽  
pp. 1-10 ◽  
Author(s):  
A. Javadian ◽  
E. Sorouri ◽  
G. H. Kim ◽  
M. Eshaghi Gordji
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Linear Differential Equation ◽  
Open Interval ◽  
Second Order ◽  
Linear Differential Equations ◽  
Ulam Stability ◽  
Order Linear Differential Equation ◽  
Order Linear ◽  
Linear Differential

We prove the generalized Hyers-Ulam stability of the 2nd-order linear differential equation of the form , with condition that there exists a nonzero in such that and is an open interval. As a consequence of our main theorem, we prove the generalized Hyers-Ulam stability of several important well-known differential equations.

A mechanical method for the solution of second-order linear differential equations

1931 ◽  
Vol 27 (4) ◽  
pp. 546-552 ◽  
Author(s):  
E. C. Bullard ◽  
P. B. Moon
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Order Differential Equation ◽  
Second Order ◽  
Linear Differential Equations ◽  
Mechanical Method ◽  
Order Linear ◽  
Second Order Differential Equation ◽  
Linear Differential

A mechanical method of integrating a second-order differential equation, with any boundary conditions, is described and its applications are discussed.

On the Nature of the Spectrum of Singular Second Order Linear Differential Equations

1951 ◽  
Vol 3 ◽  
pp. 335-338 ◽  
Author(s):  
E. A. Coddington ◽  
N. Levinson
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Continuous Functions ◽  
Second Order ◽  
Real Parameter ◽  
Linear Differential Equations ◽  
Order Linear ◽  
The Real ◽  
Linear Differential

Let p(x) > 0, q(x) be two real-valued continuous functions on . Suppose that the differential equation with the real parameter λ

The Approximate Calculation of Eigenvalues for Certain Second-Order Linear Differential Equations

1961 ◽  
Vol 65 (605) ◽  
pp. 360-360 ◽  
Author(s):  
W. J. Goodey
Keyword(s):  
Approximate Solution ◽  
Differential Equations ◽  
Simple Formula ◽  
Approximate Calculation ◽  
Technical Note ◽  
Second Order ◽  
Numerical Results ◽  
Linear Differential Equations ◽  
Order Linear ◽  
Linear Differential

In a recent technical note, Squire discussed the approximate solution of certain second-order linear differential equations by the method attributed variously to Riccati, Madelung, Wentzel, Kramers and Brillouin (the W.K.B. method), and others. The problem of eigenvalues, frequently met with in this type of equation, does not, however, appear to have received much attention by this method, and in this note a simple formula is developed which appears to give excellent numerical results in many cases.

Oscillation of neutral second order half-linear differential equations without commutativity in deviating arguments

2017 ◽  
Vol 67 (3) ◽  
Author(s):  
Simona Fišnarová ◽  
Robert Mařík
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Second Order ◽  
Neutral Differential Equation ◽  
Linear Differential Equations ◽  
Deviating Arguments ◽  
Oscillation Criteria ◽  
Linear Differential

AbstractIn this paper we derive oscillation criteria for the second order half-linear neutral differential equationwhere Φ(

Uniformly almost periodic solutions of non-linear differential equations of the second order I. General exposition

1955 ◽  
Vol 51 (4) ◽  
pp. 604-613
Author(s):  
Chike Obi
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Second Order ◽  
Linear Differential Equations ◽  
Almost Periodic ◽  
Non Linear ◽  
Independent Variable ◽  
Linear Differential ◽  
The Given ◽  
Analytical Expressions

1·1. A general problem in the theory of non-linear differential equations of the second order is: Given a non-linear differential equation of the second order uniformly almost periodic (u.a.p.) in the independent variable and with certain disposable constants (parameters), to find: (i) the non-trivial relations between these parameters such that the given differential equation has a non-periodic u.a.p. solution; (ii) the number of periodic and non-periodic u.a.p. solutions which correspond to each such relation; and (iii) explicit analytical expressions for the u.a.p. solutions when they exist.

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