Singular perturbation of linear systems with a regular singularity
The paper is devoted to the study of singularly perturbed inhomogeneous linear systems of the form \[ \varepsilon zx'= A(z,\varepsilon) x- f(z,\varepsilon), \] having a regular singularity at the origin. Summability properties of the unique formal solution, which is a power series with respect to the variable \(z\) and the perturbation parameter \(\varepsilon\), are investigated. Finally, it is shown that the series, regarded as a power series in \(\varepsilon\) with coefficients depending on \(z\), is 1-summable under a suitable and sharp eigenvalue condition.
scientific article; zbMATH DE number 1845279