The periodic problem for the second order integro-differential equations with distributed deviation
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...
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| Format: | Article |
| Language: | English |
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Institute of Mathematics of the Czech Academy of Science
2021-07-01
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| Series: | Mathematica Bohemica |
| Subjects: | |
| Online Access: | http://mb.math.cas.cz/full/146/2/mb146_2_5.pdf |
| _version_ | 1818457244976545792 |
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| author | Sulkhan Mukhigulashvili Veronika Novotná |
| author_facet | Sulkhan Mukhigulashvili Veronika Novotná |
| author_sort | Sulkhan Mukhigulashvili |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-14T22:39:29Z |
| format | Article |
| id | doaj.art-49db469a707543678e1080e8e70b81d9 |
| institution | Directory Open Access Journal |
| issn | 0862-7959 2464-7136 |
| language | English |
| last_indexed | 2024-12-14T22:39:29Z |
| publishDate | 2021-07-01 |
| publisher | Institute of Mathematics of the Czech Academy of Science |
| record_format | Article |
| series | Mathematica Bohemica |
| spelling | doaj.art-49db469a707543678e1080e8e70b81d92022-12-21T22:45:00ZengInstitute of Mathematics of the Czech Academy of ScienceMathematica Bohemica0862-79592464-71362021-07-01146216718310.21136/MB.2020.0061-19MB.2020.0061-19The periodic problem for the second order integro-differential equations with distributed deviationSulkhan MukhigulashviliVeronika NovotnáWe 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.http://mb.math.cas.cz/full/146/2/mb146_2_5.pdf linear integro-differential equation periodic problem distributed deviation solvability |
| spellingShingle | Sulkhan Mukhigulashvili Veronika Novotná The periodic problem for the second order integro-differential equations with distributed deviation Mathematica Bohemica linear integro-differential equation periodic problem distributed deviation solvability |
| title | The periodic problem for the second order integro-differential equations with distributed deviation |
| title_full | The periodic problem for the second order integro-differential equations with distributed deviation |
| title_fullStr | The periodic problem for the second order integro-differential equations with distributed deviation |
| title_full_unstemmed | The periodic problem for the second order integro-differential equations with distributed deviation |
| title_short | The periodic problem for the second order integro-differential equations with distributed deviation |
| title_sort | periodic problem for the second order integro differential equations with distributed deviation |
| topic | linear integro-differential equation periodic problem distributed deviation solvability |
| url | http://mb.math.cas.cz/full/146/2/mb146_2_5.pdf |
| work_keys_str_mv | AT sulkhanmukhigulashvili theperiodicproblemforthesecondorderintegrodifferentialequationswithdistributeddeviation AT veronikanovotna theperiodicproblemforthesecondorderintegrodifferentialequationswithdistributeddeviation AT sulkhanmukhigulashvili periodicproblemforthesecondorderintegrodifferentialequationswithdistributeddeviation AT veronikanovotna periodicproblemforthesecondorderintegrodifferentialequationswithdistributeddeviation |