A note on singular nonlinear two-point boundary-value problems (Q1961261)

The authors consider the following nonlinear twopoint boundary value problems: \[ -y''(t) = p(t) f(y(t)) + q(t), \quad t \in (0,1), \qquad y(0)=A, \quad y(1) = \xi, \] and \[ -y''(t) = p(t) f(y(t)) + q(t), \quad t \in (0,1), \qquad y(0)=A, \quad y'(1) = B. \] Under suitable conditions on \(p\), \(q\), \(f\), \(A\), \(B\) and \(\xi\), which allow some kind of singularities in the functions \(f\), \(p\) and \(q\), they prove the existence of a unique nonnegative solution in both cases.