On the stability problem of differential equations in the sense of Ulam

DOI10.1007/s00025-019-1132-6zbMath1439.34061OpenAlexW2993636877WikidataQ112879307 ScholiaQ112879307MaRDI QIDQ2302199

Süleyman Öğrekçi, Yasemin Başcı, Adil Misir

Publication date: 25 February 2020

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

Full work available at URL: https://doi.org/10.1007/s00025-019-1132-6

zbMATH Keywords

fixed point theoryHyers-Ulam-Rassias stabilitydifferential equationsstability theorygeneralized metric spaces

Mathematics Subject Classification ID

Perturbations of ordinary differential equations (34D10) Applications of operator theory to differential and integral equations (47N20)

Related Items

Ulam-Hyers-Rassias stability of nonlinear differential equations with Riemann-Liouville fractional derivative ⋮ Stability results of some fractional neutral integrodifferential equations with delay ⋮ Ulam stability of dynamic equations on time scales ⋮ A fixed point method for stability of nonlinear volterra integral equations in the sense of Ulam ⋮ Unnamed Item ⋮ Ulam-Hyers-Rassias stability of stochastic functional differential equations via fixed point methods ⋮ Hyers-Ulam-Rassias stability of the generalized fractional systems and the \(\rho\)-Laplace transform method ⋮ A new approach to the Hyers-Ulam-Rassias stability of differential equations ⋮ Mittag-Leffler-Hyers-Ulam stability of delay fractional differential equation via fractional Fourier transform ⋮ Ulam type stability for conformable fractional differential equations

Cites Work

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• Hyers-Ulam stability of Euler's differential equation
• Ulam-Hyers stability for operatorial equations and inclusions via nonself operators
• The Ulam stability of first order linear dynamic equations on time scales
• Fixed point methods for the generalized stability of functional equations in a single variable
• Stability theory and the existence of periodic solutions and almost periodic solutions
• On some inequalities and stability results related to the exponential function
• A characterization of Hyers-Ulam stability of first order linear differential operators.
• Comments on the core of the direct method for proving Hyers-Ulam stability of functional equations
• On Hyers-Ulam stability of Hosszú's functional equation
• Ulam-Hyers-Rassias stability for a class of fractional integro-differential equations
• Hyers-Ulam stability of general Jensen-type mappings in Banach algebras
• Hyers--Ulam--Rassias stability of a linear recurrence
• The Hyers-Ulam stability of nonlinear recurrences
• On the stability of the linear transformation in Banach spaces
• A fixed point approach to the stability of differential equations \(y'=F(x,y)\)
• Note on the stability of first order linear differential equations
• ON THE HYERS-ULAM STABILITY OF THE BANACH SPACE-VALUED DIFFERENTIAL EQUATION y'=λy
• On the Stability of the Linear Mapping in Banach Spaces
• Hyers–Ulam stability of linear differential operator with constant coefficients
• A fixed point theorem of the alternative, for contractions on a generalized complete metric space
• On the Stability of the Linear Functional Equation