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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

Singular Perturbation of Nonlinear Systems with Regular Singularity

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Author(s):
Marchetti, Domingos H. U. [1] ; Conti, William R. P. [2]
Total Authors: 2
Affiliation:
[1] Univ Sao Paulo, Inst Fis, Rua Matao 1371, BR-05508090 Sao Paulo, SP - Brazil
[2] Univ Fed Sao Paulo, Dept Ciencias Mar, Rua Dr Carvalho Mendonca 144, BR-11070100 Santos, SP - Brazil
Total Affiliations: 2
Document type: Journal article
Source: DISCRETE DYNAMICS IN NATURE AND SOCIETY; 2018.
Web of Science Citations: 0
Abstract

We extend Balser-Kostov method of studying summability properties of a singularly perturbed inhomogeneous linear system with regular singularity at origin to nonlinear systems of the form epsilon zf' = F(epsilon, z, f) with F a C-nu-valued function, holomorphic in a polydisc (D-rho) over barx (D-rho) over barx (D) over bar (nu). We show that its unique formal solution in power series of epsilon, whose coefficients are holomorphic functions of z, is 1-summ able under a Siegel-type condition on the eigenvalues of F-f(0, 0, 0). The estimates employed resemble the ones used in KAM theorem. A simple lemma is applied to tame convolutions that appear in the power series expansion of nonlinear equations. Applications to spherical Bessel functions and probability theory are indicated. The proposed summability method has certain advantages as it may be applied as well to (singularly perturbed) nonlinear partial differential equations of evolution type. (AU)