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 |