On three solutions of the second order periodic boundary-value problem
We consider the periodic boundary-value problem x'' + a(t)x' + b(t)x = f(t, x, x'), x(') =x(2π), x'(0) = x' (2π), where a, b are Lebesgue integrable functions and f fulfils the
 Caratheodory conditions. We extend results about the Leray – Schauder topolog...
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| Published in: | Нелінійні коливання |
|---|---|
| Date: | 2001 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2001
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/174763 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | On three solutions of the second order periodic boundary-value problem / J. Draessler, I. Rachůnková // Нелінійні коливання. — 2001. — Т. 4, № 3. — С. 471-486. — Бібліогр.: 6 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862533873812897792 |
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| author | Draessler, J. Rachůnková, I. |
| author_facet | Draessler, J. Rachůnková, I. |
| citation_txt | On three solutions of the second order periodic boundary-value problem / J. Draessler, I. Rachůnková // Нелінійні коливання. — 2001. — Т. 4, № 3. — С. 471-486. — Бібліогр.: 6 назв. — англ. |
| collection | DSpace DC |
| container_title | Нелінійні коливання |
| description | We consider the periodic boundary-value problem x'' + a(t)x' + b(t)x = f(t, x, x'), x(') =x(2π), x'(0) = x' (2π), where a, b are Lebesgue integrable functions and f fulfils the
Caratheodory conditions. We extend results about the Leray – Schauder topological degree and ´ present conditions implying nonzero values of the degree on sets defined by lower and upper
functions. Using such results we prove the existence of at least three different solutions to the
above problem.
|
| first_indexed | 2025-11-24T06:44:33Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-174763 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-3076 |
| language | English |
| last_indexed | 2025-11-24T06:44:33Z |
| publishDate | 2001 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Draessler, J. Rachůnková, I. 2021-01-27T18:14:01Z 2021-01-27T18:14:01Z 2001 On three solutions of the second order periodic boundary-value problem / J. Draessler, I. Rachůnková // Нелінійні коливання. — 2001. — Т. 4, № 3. — С. 471-486. — Бібліогр.: 6 назв. — англ. 1562-3076 AMS Subject Classification: 34B15, 34C25 https://nasplib.isofts.kiev.ua/handle/123456789/174763 We consider the periodic boundary-value problem x'' + a(t)x' + b(t)x = f(t, x, x'), x(') =x(2π), x'(0) = x' (2π), where a, b are Lebesgue integrable functions and f fulfils the
 Caratheodory conditions. We extend results about the Leray – Schauder topological degree and ´ present conditions implying nonzero values of the degree on sets defined by lower and upper
 functions. Using such results we prove the existence of at least three different solutions to the
 above problem. Supported by grant No. 201/01/1451 of the Grant Agency of Czech Republic. en Інститут математики НАН України Нелінійні коливання On three solutions of the second order periodic boundary-value problem Про три розв'язки періодичної крайової задачі другого порядку О трех решениях периодической краевой задачи второго порядка Article published earlier |
| spellingShingle | On three solutions of the second order periodic boundary-value problem Draessler, J. Rachůnková, I. |
| title | On three solutions of the second order periodic boundary-value problem |
| title_alt | Про три розв'язки періодичної крайової задачі другого порядку О трех решениях периодической краевой задачи второго порядка |
| title_full | On three solutions of the second order periodic boundary-value problem |
| title_fullStr | On three solutions of the second order periodic boundary-value problem |
| title_full_unstemmed | On three solutions of the second order periodic boundary-value problem |
| title_short | On three solutions of the second order periodic boundary-value problem |
| title_sort | on three solutions of the second order periodic boundary-value problem |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/174763 |
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