Consider the boundary value problem Lu ≡ -(pu')' + qu' + ru = f, a ≤ x ≤ b, u(a) = u(b) = 0. Let H_νA_νU = f and be its finite difference equations and piecewise linear finite element equations on partitions , ν = 1, 2,… with , as ν → ∞, where H_ν are n_ν  n_ν diagonal matrices and A_ν as well as are n_ν  n_ν tridiagonal. It is shown that the following three conditions are equivalent: (i) The boundary value problem has a unique solution u ∈ C²[a, b]. (ii) For sufficiently large ν ≥ ν₀, the inverse exists and , ∀ i, j with a constant M > 0 independent of h^ν. (iii) For sufficiently large ν ≥ , exists and , ∀ i, j with a constant independent of h^ν. It is also shown by a numerical example that the finite difference method with uniform nodes x_i+1 = x_i + h, 0 ≤ i ≤ n, h = (b - a)/(n + 1) applied to the boundary value problem with no solution gives a ghost solution for every n.