On solvability of three point BVPs of second order ODEs (Q1876734)

The author gives some solvability conditions by using the Leray-Schauder principle, discusses the nonresonant conditions between two resonant points and gives some related existence results for the three-point boundary value problem \[ x'' + f(t,x,x')=0, \quad x(0)=0=x(1)-x(t_1), \] where \(f:[0,1] \times \mathbb R^n \times \mathbb R^n \to \mathbb R^n\) is a continuous function, \(t_1\) is a constant and \(t_1 \in (0,1)\).