Invariance of Hyers-Ulam stability of linear differential equations and its applications

DOI10.1186/s13662-015-0617-1zbMath1351.34064OpenAlexW2169717822WikidataQ59429218 ScholiaQ59429218MaRDI QIDQ738471

Ginkyu Choi, Jung, Soon-Mo

Publication date: 2 September 2016

Published in: Advances in Difference Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/s13662-015-0617-1

zbMATH Keywords

approximationHyers-Ulam stabilitylinear differential equationgeneralized Hyers-Ulam stabilityCauchy-Euler equation

Mathematics Subject Classification ID

Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Perturbations of ordinary differential equations (34D10) Linear ordinary differential equations and systems (34A30)

Related Items (12)

Connections between Hyers-Ulam stability and uniform exponential stability of 2-periodic linear nonautonomous systems ⋮ Approximation of analytic functions by solutions of Cauchy-Euler equation ⋮ Hyers-Ulam stability of first-order homogeneous linear differential equations with a real-valued coefficient ⋮ On some conformable boundary value problems in the setting of a new generalized conformable fractional derivative ⋮ Hyers-Ulam stability of the first-order matrix differential equations ⋮ Unnamed Item ⋮ Hyers-Ulam-Rassias stability of non-linear delay differential equations ⋮ The linear differential equations with complex constant coefficients and Schrödinger equations ⋮ Ulam's type stability of higher order nonlinear delay differential equations via integral inequality of Grönwall-Bellman-Bihari's type ⋮ Existence theory and Ulam's stabilities of fractional Langevin equation ⋮ Perturbation of the one-dimensional time-independent Schrödinger equation with a rectangular potential barrier ⋮ Hyers-Ulam stability for second order linear differential equations of Carathéodory type

Cites Work

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• On the Hyers-Ulam stability of the linear differential equation
• On the stability of the linear differential equation of higher order with constant coefficients
• Hyers-Ulam stability of linear differential equations of second order
• Hyers-Ulam stability of linear differential equations of first order
• On approximate Euler differential equations
• Hyers-Ulam stability of nonhomogeneous linear differential equations of second order
• On some inequalities and stability results related to the exponential function
• On the Hyers-Ulam stability of differential equations of second order
• Hyers-Ulam stability of linear differential equations of first order.
• Hyers-Ulam stability of the linear differential operator with nonconstant coefficients
• The inhomogeneous Euler equation and its Hyers-Ulam stability
• Hyers-Ulam stability of linear differential equations of first order. II
• Hyers-Ulam stability of exact second-order linear differential equations
• Hyers-Ulam stability of a system of first order linear differential equations with constant coefficients
• ON THE HYERS-ULAM STABILITY OF THE BANACH SPACE-VALUED DIFFERENTIAL EQUATION y'=λy
• HYERS-ULAM-RASSIAS STABILITY OF THE BANACH SPACE VALUED LINEAR DIFFERENTIAL EQUATIONS y′ = λy
• ON HYERS-ULAM STABILITY OF NONLINEAR DIFFERENTIAL EQUATIONS
• Hyers-Ulam stability of the first order linear differential equation for Banach space-valued holomorphic mappings
• Stability of functional equations in several variables
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