Positive Solutions for Second-order Boundary Value Problem with Integral Boundary Conditions at Resonance on a Half-line

This paper deals with the second order boundary value problem with integral boundary conditions on a half-line: (p(t)x′(t))′ + g(t)f(t, x(t)) = 0, a.e. in (0,∞), x(0) = ∫ ∞ 0 x(s)g(s)ds, lim t→∞ p(t)x′(t) = p(0)x′(0). A new result on the existence of positive solutions is obtained. The interesting points are: firstly, the boundary value problem involved in the integral boundary condition on unbounded domains; secondly, we employ a new tool – the recent Leggett-Williams norm-type theorem for coincidences and obtain positive solutions. Also, an example is constructed to illustrate that our result here is valid.