The authors establish existence results on solutions to the nonlinear three-point boundary value problem
where is a given constant, is continuous, is continuous and possibly nonlinear. Their theory incorporates a degree-based relationship between the boundary conditions and the lower and upper solutions. For earlier results on the nonlinear equation with some linear multipoint boundary conditions, see R. Ma [J. Math. Anal. Appl. 211, No. 2, 545-555 (1997; Zbl 0884.34024)].