Primary 34B15.

Herein, we consider the existence of solutions to second-order systems of two-point boundary value problems (BVPs). The methods used involve the topological transversality approach of Granas et. al. combined with a Bernstein-Nagumo condition from Gaines and Mawhin. The new results allow the treatment of systems of BVPs without growth restrictions in the third variable. The new results also are applicable to systems of BVPs that may have singularities in the right-hand side at the end-points of the interval of existence. Some examples are presented to illustrate the theory.;