Summary: A boundary value problem on the half-line to a class of second-order differential equations is considered. In particular, the existence of solutions which start at the origin, are positive on the real half-line and tend to a nonzero constant as \(t\) tends to infinity, is studied. The solvability of this BVP is accomplished by a new approach which combines, in a suitable way, two separated problems on \([0,1[\) and \([1,\infty)\) and uses some continuity arguments.