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 topological deg...
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| Published in: | Нелінійні коливання |
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| Date: | 2001 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
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| Summary: | 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.
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| ISSN: | 1562-3076 |