Ulam type stabilities of \(n\)-th order linear differential equations using Gronwall's inequality

DOI10.1007/s00025-023-01975-7zbMath1522.34034OpenAlexW4385604059MaRDI QIDQ6171703

Arumugam Ponmana Selvan, Masakazu Onitsuka

Publication date: 14 August 2023

Published in: Results in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00025-023-01975-7

zbMATH Keywords

Hyers-Ulam-Rassias stabilityHyers-Ulam stabilitylinear differential equationGronwall's inequalityMittag-Leffler-Hyers-Ulam stabilityMittag-Leffler-Hyers-Ulam-Rassias stabilityreplacement lemma

Mathematics Subject Classification ID

Perturbations of ordinary differential equations (34D10) Linear ordinary differential equations and systems (34A30) Inequalities for sums, series and integrals (26D15)

Cites Work

• Hyers-Ulam stability of first-order homogeneous linear differential equations with a real-valued coefficient
• Approximate solutions of a linear differential equation of third order
• On the Hyers-Ulam stability of the linear differential equation
• Hyers-Ulam stability of linear differential equations of second order
• On some inequalities and stability results related to the exponential function
• A characterization of Hyers-Ulam stability of first order linear differential operators.
• On the Hyers-Ulam stability of real continuous function valued differentiable map
• Hyers-Ulam stability of first order linear differential equations of Carathéodory type and its application
• Hyers-Ulam stability of linear differential equations of first order.
• Hyers-Ulam stability for a class of perturbed Hill's equations
• Hyers-Ulam stability of first-order linear differential equations using Aboodh transform
• Ulam stability of linear differential equations using Fourier transform
• Hyers-Ulam stability for differential systems with \(2\times 2\) constant coefficient matrix
• Aboodh transform and the stability of second order linear differential equations
• Hyers-Ulam stability of the linear differential operator with nonconstant coefficients
• Ulam stability of operators
• 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 linear differential equations of first order. III
• Best constant in Hyers-Ulam stability of first-order homogeneous linear differential equations with a periodic coefficient
• On the stability of the linear transformation in Banach spaces
• ON THE HYERS-ULAM STABILITY OF THE BANACH SPACE-VALUED DIFFERENTIAL EQUATION y'=λy
• Hyers-Ulam stability of n ͭ ͪ order linear differential equation
• On the Stability of the Linear Mapping in Banach Spaces
• HYERS-ULAM-RASSIAS STABILITY OF THE BANACH SPACE VALUED LINEAR DIFFERENTIAL EQUATIONS y′ = λy
• Mahgoub transform and Hyers-Ulam stability of first-order linear differential equations
• Classes of transformations and bordering transformations
• On the Stability of the Linear Functional Equation
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