Positive solutions of nonlocal continuous second order BVP'S

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 a compact and on a noncompact interval and uses some continuity arguments.