Triple positive solutions for a class of two-point boundary-value problems. A fundamental approach
In this paper, we prove the existence of three positive and concave solutions, by means of an elementary simple approach, to the 2th order two-point boundary-value problem x''(t) = α(t)f(t, x(t), x'(t)), 0 < t < 1, x(0) = x(1) = 0,. We rely on a combination of the analysis of...
Збережено в:
| Дата: | 2012 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2012
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| Назва видання: | Нелінійні коливання |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/175589 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Triple positive solutions for a class of two-point boundary-value problems. A fundamental approach / P.K. Palamides, A.P. Palamides // Нелінійні коливання. — 2012. — Т. 15, № 2. — С. 233-243. — Бібліогр.: 21 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Резюме: | In this paper, we prove the existence of three positive and concave solutions, by means of an elementary
simple approach, to the 2th order two-point boundary-value problem
x''(t) = α(t)f(t, x(t), x'(t)), 0 < t < 1, x(0) = x(1) = 0,.
We rely on a combination of the analysis of the corresponding vector field on the phase-space along with
Kneser’s type properties of the solutions funnel and the Schauder’s fixed point theorem. The obtained
results justify the simplicity and efficiency (one could study the problem with more general boundary
conditions) of our new approach compared to the commonly used ones, like the Leggett – Williams Fixed
Point Theorem and its generalizations. |
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