On a singular boundary value problem

AbstractThe purpose of this paper is to establish sufficient conditions for the existence and uniqueness of solution of the boundary value problem u″ = f(t, u, u′); (1) limt→0u(t)=0, limt→1u(t)=0. (2) It is assumed that the function f(t, x, y) is defined on the domain 0 < t < 1, −∞ < x, y < +∞, measurable in t for every x, y ϵ (−∞, +∞) and continuous in x, y for almost every t ϵ (0, 1). Furthermore, the case is admitted when f(t, x, y) has singularities for t = 0 and t = 1 and is nonsummable with respect to t on the interval (0, 1). In this sense the considered problem is singular