HYERS-ULAM STABILITY FOR AN NTH ORDER DIFFERENTIAL EQUATION USING FIXED POINT APPROACH

被引：16

作者：

Murali, Ramdoss ^{[1
]}

Park, Choonkil ^{[2
]}

Selvan, Arumugam Ponmana ^{[1
]}

机构：

[1] Sacred Heart Coll Autonomous, PG & Res Dept Math, Tirupattur 635601, Tamil Nadu, India

[2] Hanyang Univ, Res Inst Nat Sci, Seoul 04763, South Korea

来源：

JOURNAL OF APPLIED ANALYSIS AND COMPUTATION | 2021年 / 11卷 / 02期

关键词：

Hyers-Ulam stability; Hyers-Ulam-Rassias stability; fixed point method; differential equation;

D O I：

10.11948/20190093

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we prove the Hyers-Ulam stability and the HyersUlam-Rassias stability of the nth order differential equation of the form x((n))(t) = f(t, x(t)) and x((n))(t) = f (t, x(t), x' (t), x '' (t), ..., x((n-1))(t)) with initial conditions x(a) = x(0), x' (a) = x(1), x '' (a) = x(2), ..., x((n-1))(a) = x(n-1) for all t is an element of I = [a, b] subset of R and x is an element of C-(n)( I) by using fixed point method in the sense of Cadariu and Radu.

引用

页码：614 / 631

页数：18

共 29 条

[11] Asymptotic problems for functional differential equations via linearization method [J].

Dosla, Zuzana ;

Liska, Petr ;

Marini, Mauro .

JOURNAL OF FIXED POINT THEORY AND APPLICATIONS, 2019, 21 (01)

[12]

Gavruta P, 2010, INT J NONLINEAR ANAL, V1, P11

[13]

Gavruta P, 2011, ELECTRON J DIFFER EQ

[14] On the stability of the linear functional equation [J].

Hyers, DH .

PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 1941, 27 :222-224

[15] A fixed point approach to the stability of isometries [J].

Jung, Soon-Mo .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2007, 329 (02) :879-890

[16] Hyers-Ulam stability of a system of first order linear differential equations with constant coefficients [J].

Jung, Soon-Mo .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2006, 320 (02) :549-561

[17]

Jung SM, 2010, B MALAYS MATH SCI SO, V33, P47

[18] Hyers-Ulam stability of nth order linear differential equations [J].

Li, Tongxing ;

Zada, Akbar ;

Faisal, Shah .

JOURNAL OF NONLINEAR SCIENCES AND APPLICATIONS, 2016, 9 (05) :2070-2075

[19]

Miljanovic J. K., 2014, GEN MATH NOTES, V20, P27

[20]

Murali R, 2018, KRAGUJEV J MATH, V42, P579

← 1 2 3 →