Geodesic
The periodic problem for the second order integro-differential equations with distributed deviation
Mathematica Bohemica, Tome 146 (2021) no. 2, pp. 167-183 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

We study the question of the unique solvability of the periodic type problem for the second order linear integro-differential equation with distributed argument deviation $$ u''(t)=p_0(t)u(t)+\int _{0}^{\omega }p(t,s)u(\tau (t,s)) {\rm d}s+ q(t), $$ and on the basis of the obtained results by the a priori boundedness principle we prove the new results on the solvability of periodic type problem for the second order nonlinear functional differential equations, which are close to the linear integro-differential equations. The proved results are optimal in some sense.
We study the question of the unique solvability of the periodic type problem for the second order linear integro-differential equation with distributed argument deviation $$ u''(t)=p_0(t)u(t)+\int _{0}^{\omega }p(t,s)u(\tau (t,s)) {\rm d}s+ q(t), $$ and on the basis of the obtained results by the a priori boundedness principle we prove the new results on the solvability of periodic type problem for the second order nonlinear functional differential equations, which are close to the linear integro-differential equations. The proved results are optimal in some sense.
DOI : 10.21136/MB.2020.0061-19
Classification : 34B15, 34K06, 34K13
Keywords: linear integro-differential equation; periodic problem; distributed deviation; solvability 
@article{10_21136_MB_2020_0061_19,
     author = {Mukhigulashvili, Sulkhan and Novotn\'a, Veronika},
     title = {The periodic problem for the second order integro-differential equations with distributed deviation},
     journal = {Mathematica Bohemica},
     pages = {167--183},
     year = {2021},
     volume = {146},
     number = {2},
     doi = {10.21136/MB.2020.0061-19},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/MB.2020.0061-19/}
}
TY  - JOUR
AU  - Mukhigulashvili, Sulkhan
AU  - Novotná, Veronika
TI  - The periodic problem for the second order integro-differential equations with distributed deviation
JO  - Mathematica Bohemica
PY  - 2021
SP  - 167
EP  - 183
VL  - 146
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.21136/MB.2020.0061-19/
DO  - 10.21136/MB.2020.0061-19
LA  - en
ID  - 10_21136_MB_2020_0061_19
ER  - 
%0 Journal Article
%A Mukhigulashvili, Sulkhan
%A Novotná, Veronika
%T The periodic problem for the second order integro-differential equations with distributed deviation
%J Mathematica Bohemica
%D 2021
%P 167-183
%V 146
%N 2
%U http://geodesic.mathdoc.fr/articles/10.21136/MB.2020.0061-19/
%R 10.21136/MB.2020.0061-19
%G en
%F 10_21136_MB_2020_0061_19
Mukhigulashvili, Sulkhan; Novotná, Veronika. The periodic problem for the second order integro-differential equations with distributed deviation. Mathematica Bohemica, Tome 146 (2021) no. 2, pp. 167-183. doi: 10.21136/MB.2020.0061-19

Cité par Sources :