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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| Date: | 2012 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
2012
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| Series: | Нелінійні коливання |
| Online Access: | http://dspace.nbuv.gov.ua/handle/123456789/175589 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | 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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