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...
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| Мова: | English |
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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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| 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. |
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irk-123456789-1755892021-02-02T01:28:13Z Triple positive solutions for a class of two-point boundary-value problems. A fundamental approach Palamides, P.K. Palamides, A.P. 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. З допомогою елементарного пiдходу до двоточкової граничної задачi другого порядку x''(t) = α(t)f(t, x(t), x'(t)), 0 < t < 1, x(0) = x(1) = 0,. доведено iснування трьох додатних та вгнутих розв’язкiв. При цьому використано аналiз вiдповiдного векторного поля на фазовому просторi, кнессеровськi властивостi множини розв’язкiв та теорему Шаудера про нерухому точку. Отриманi результати пояснюють простоту та ефективнiсть розробленого нового пiдходу (можливiсть вивчати задачу з бiльш загальними граничними значеннями) в порiвняннi з методами, що використовувалися ранiше, наприклад теоремою Логгетт та Вiльямса про нерухому точку та її узагальнення 2012 Article 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. 1562-3076 http://dspace.nbuv.gov.ua/handle/123456789/175589 517.9 en Нелінійні коливання Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
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. |
| format |
Article |
| author |
Palamides, P.K. Palamides, A.P. |
| spellingShingle |
Palamides, P.K. Palamides, A.P. Triple positive solutions for a class of two-point boundary-value problems. A fundamental approach Нелінійні коливання |
| author_facet |
Palamides, P.K. Palamides, A.P. |
| author_sort |
Palamides, P.K. |
| title |
Triple positive solutions for a class of two-point boundary-value problems. A fundamental approach |
| title_short |
Triple positive solutions for a class of two-point boundary-value problems. A fundamental approach |
| title_full |
Triple positive solutions for a class of two-point boundary-value problems. A fundamental approach |
| title_fullStr |
Triple positive solutions for a class of two-point boundary-value problems. A fundamental approach |
| title_full_unstemmed |
Triple positive solutions for a class of two-point boundary-value problems. A fundamental approach |
| title_sort |
triple positive solutions for a class of two-point boundary-value problems. a fundamental approach |
| publisher |
Інститут математики НАН України |
| publishDate |
2012 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/175589 |
| citation_txt |
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. |
| series |
Нелінійні коливання |
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2023-10-18T22:39:11Z |
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