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Positive solutions to a singular third-order three-point boundary value problem with an indefinitely signed Green’s function

✍ Scribed by Alex P. Palamides; George Smyrlis

Publisher
Elsevier Science
Year
2008
Tongue
English
Weight
385 KB
Volume
68
Category
Article
ISSN
0362-546X

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✦ Synopsis

We determine a Green's function for the singular three-point third-order BVP

and then we apply the classical Krasnosel'skiȋ's fixed point theorem on an also new cone. The emphasis is mainly that although this BVP does not admit a positive Green's function, the solution obtained is still positive. In our approach we find out that η ∈ 17 24 , 1 . Our technique is a combination of the above fixed point theorem and properties of the corresponding vector field.

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