The periodic problem for the second order integro-differential equations with distributed deviation

Mukhigulashvili, Sulkhan; Novotná, Veronika

The periodic problem for the second order integro-differential equations with distributed deviation

Files

MB.2020.006119.pdf(200.32 KB)

Date

2021-06-05

Authors

Mukhigulashvili, Sulkhan

Novotná, Veronika

Publisher

Institute of Mathematics CAS

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Abstract

In the paper we describe the classes of unique solvability of the Dirichlet and mixed two point boundary value problems for the second order linear integro-differential equation b u (t) = p0 (t)u(t) + p1 (t)u(1 (t)) + p(t, s)u( (s)) ds + q(t). a On the basis of the obtained and, in some sense, optimal results for the linear problems, by the a priori boundedness principle we prove the theorems of solvability and unique solvability for the second order nonlinear functional differential equations under the mentioned boundary conditions.

Keywords

Integro-differential equations, Dirichlet and mixed problems, unique solvability, a priori boundedness principle

Citation

Mathematica Bohemica. 2021, vol. 146, issue 2, p. 167-183.
https://articles.math.cas.cz/10.21136/MB.2020.0061-19

Document type

Peer-reviewed

Document version

Published version

Language of document

en

Document licence

Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/