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Positive solutions of nonlocal continuous second order BVP’s. (English) Zbl 1312.34057
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.

##### MSC:
 34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations 34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations 34B15 Nonlinear boundary value problems for ordinary differential equations