On solvability sets of boundary value problems for linear functional differential equations

Title:

On solvability sets of boundary value problems for linear functional differential equations

Creator:

Bravyi, Eugene

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:ef62ecd7-802c-4942-abd9-d0fb5813b116
uuid:ef62ecd7-802c-4942-abd9-d0fb5813b116
doi:10.21136/MB.2011.141577

Subject:

functional differential equation, boundary value problem, and periodic problem

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

Consider boundary value problems for a functional differential equation ( x (n) (t) = (T +x)(t) − (T −x)(t) + f(t), t ∈ [a, b], lx = c, where T +, T − : C[a, b] → L[a, b] are positive linear operators; l: ACn−1 [a, b] → R n is a linear bounded vector-functional, f ∈ L[a, b], c ∈ ℝ n , n ≥ 2. Let the solvability set be the set of all points (T +, T −) ∈ ℝ + 2 such that for all operators T +, T − with kT ±kC→L = T ± the problems have a unique solution for every f and c. A method of finding the solvability sets are proposed. Some new properties of these sets are obtained in various cases. We continue the investigations of the solvability sets started in R. Hakl, A. Lomtatidze, J. Šremr: Some boundary value problems for first order scalar functional differential equations. Folia Mathematica 10, Brno, 2002.

Language:

English

Rights:

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

Coverage:

145-154

Source:

Mathematica bohemica | 2011 Volume:136 | Number:2

Harvested from:

CDK

Metadata only:

false