Chebyshev’s differential equation and its Hyers-Ulam stability. (English) Zbl 1181.34013

From the introduction: We investigate the general solution of the inhomogeneous Chebyshev’s differential equation of the form
\[ (1-x^2)y''(x)-xy'(x)+n^2y(x)=\sum^\infty_{m=0}a_mx^m,\tag{1} \]
where \(n\) is a given positive integer. We give a partial solution of the Hyers-Ulam stability problem for the Chebyshev differential equation (2) in a subclass of analytic functions.


34A30 Linear ordinary differential equations and systems
34D99 Stability theory for ordinary differential equations
34A40 Differential inequalities involving functions of a single real variable
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