On a Nonlocal Boundary Value Problem for Second Order Linear Ordinary Differential Equations

Existence and uniqueness criteria are established for the solution of the equation u″ = p1(t)u + p2(t)u′ + p0(t), satisfying the boundary conditions u(a+) = c1, u(b−) = ∫bau(x) dμ(x) + c2, where the coefficients pk :]a, b[→ R (k = 0, 1, 2) are locally integrable and μ: [a, b] → R is a function of bounded variation. These criteria include the case when the functions pk :]a, b[→ R (k = 0, 1, 2) are not integrable on [a, b], having singularities in a and b.