A note on a second order three-point boundary value problem (Q1336190)

The existence problem for the BVP \(x'' = f(t,x,x')\), \(x(0) = 0\), \(x(\eta) = x(1)\), \(t \in[0,1]\) is considered. Employing Leray-Schauder continuation theorem and Wirtinger type inequalities, the author gives another (and more simple) proof of some results established very recently in [\textit{S. A. Marano}, J. Math. Anal. Appl. 183, No. 3, 518-522 (1994; Zbl 0801.34025)].