Sun, Yong-Ping2021-05-032021-05-032004-09-22Sun, Y. P. (2004). Nontrivial solution for a three-point boundary-value problem. <i>Electronic Journal of Differential Equations, 2004</i>(111), pp. 1-10.1072-6691https://hdl.handle.net/10877/13484In this paper, we study the existence of nontrivial solutions for the second-order three-point boundary-value problem u'' + ƒ(t, u) = 0, 0 < t < 1, u'(0) = 0, u(1) = ɑu'(η). where η ∈ (0, 1), ɑ ∈ ℝ, ƒ ∈ C([0, 1] x ℝ, ℝ). Under certain growth conditions on the nonlinearity ƒ and by using Leray-Schauder nonlinear alternative, sufficient conditions for the existence of nontrivial solution are obtained. We illustrate the results obtained with some examples.Text10 pages1 file (.pdf)enAttribution 4.0 InternationalThree-point boundary-value problemNontrivial solutionLeray-Schauder nonlinear alternativeArticle