On the opial type criterion for the well-posedness of the Cauchy problem for linear systems of generalized ordinary differential equations

Title:

On the opial type criterion for the well-posedness of the Cauchy problem for linear systems of generalized ordinary differential equations

Creator:

Ashordia, Malkhaz

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:575aadd6-7212-43a8-b362-68a102804261
uuid:575aadd6-7212-43a8-b362-68a102804261
doi:10.21136/MB.2016.15

Subject:

linear system of generalized ordinary differential equations in the Kurzweil sense, Cauchy problem, well-posedness, Opial type sufficient condition, and efficient sufficient condition

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

The Cauchy problem for the system of linear generalized ordinary differential equations in the J. Kurzweil sense dx(t) = dA0(t) · x(t) + df0(t), x(t0) = c0 (t ∈ I) with a unique solution x0 is considered. Necessary and sufficient conditions are obtained for a sequence of the Cauchy problems dx(t) = dAk(t) · x(t) + dfk(t), x(tk) = ck (k = 1, 2, . . .) to have a unique solution xk for any sufficiently large k such that xk(t) → x0(t) uniformly on I. Presented results are analogous to the sufficient conditions due to Z. Opial for linear ordinary differential systems. Moreover, efficient sufficient conditions for the problem of well-posedness are given.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

183-215

Source:

Mathematica bohemica | 2016 Volume:141 | Number:2

Harvested from:

CDK

Metadata only:

false