Palamides, Alex P.Veloni, Anastasia2021-08-182021-08-182007-11-13Palamides, A. P., & Veloni, A. N. (2007). A singular third-order 3-point boundary-value problem with nonpositive Green's function. <i>Electronic Journal of Differential Equations, 2007</i>(151), pp. 1-13.1072-6691https://hdl.handle.net/10877/14365We 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.Text13 pages1 file (.pdf)enAttribution 4.0 InternationalThree-point singular boundary-value problemFixed point in conesThird-order differential equationPositive solutionGreen's functionVector fieldArticle