# A singular third-order 3-point boundary-value problem with nonpositive Green's function

 dc.contributor.author Palamides, Alex P. dc.contributor.author Veloni, Anastasia dc.date.accessioned 2021-08-18T15:42:36Z dc.date.available 2021-08-18T15:42:36Z dc.date.issued 2007-11-13 dc.description.abstract We find a Green's function for the singular third-order three-point BVP u‴(t) = -α(t)ƒ(t, u(t)), u(0) = u′(1) = u″(η) = 0 where 0 ≤ η < 1/2. Then we apply the classical Krasnosel'skii's fixed point theorem for finding solutions in a cone. Although this problem Green's function is not positive, the obtained solution is still positive and increasing. Our techniques rely on a combination of a fixed point theorem and the properties of the corresponding vector field. dc.description.department Mathematics dc.format Text dc.format.extent 13 pages dc.format.medium 1 file (.pdf) dc.identifier.citation Palamides, A. P., & Veloni, A. N. (2007). A singular third-order 3-point boundary-value problem with nonpositive Green's function. Electronic Journal of Differential Equations, 2007(151), pp. 1-13. dc.identifier.issn 1072-6691 dc.identifier.uri https://hdl.handle.net/10877/14365 dc.language.iso en dc.publisher Texas State University-San Marcos, Department of Mathematics dc.rights Attribution 4.0 International dc.rights.uri https://creativecommons.org/licenses/by/4.0/ dc.source Electronic Journal of Differential Equations, 2007, San Marcos, Texas: Texas State University-San Marcos and University of North Texas. dc.subject Three-point singular boundary-value problem dc.subject Fixed point in cones dc.subject Third-order differential equation dc.subject Positive solution dc.subject Green's function dc.subject Vector field dc.title A singular third-order 3-point boundary-value problem with nonpositive Green's function en_US dc.type Article

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