The author studies the existence of solutions to the second-order three-point boundary value problem
where is continuous, , and are given constants such that . The proof of the main result is based upon the connectivity properties of parameterized families of compact vector fields.
For related work, see R. Ma [Nonlinear Anal., Theory Methods Appl. 53 A, No. 6, 777–789 (2003; Zbl 1037.34011)].