| Full text | |
| Author(s): |
Marchetti, Domingos H. U.
;
Conti, William R. P.
Total Authors: 2
|
| Document type: | Journal article |
| Source: | DISCRETE DYNAMICS IN NATURE AND SOCIETY; v. 2018, p. 10-pg., 2018-01-01. |
| 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) | |