Singular continuous spectrum of half-line Schrodinger operators with point interactions on a sparse set

We say that a discrete set X = {xn}n ∈ N0 on the half-line 0 = x0 < x1 < x2 < x3 < ⋅ ⋅ ⋅< xn < ⋅ ⋅ ⋅,< +∞ is sparse if the distances Δxn = xn+1-xn between neighbouring points satisfy the condition [formula]. In this paper half-line Schrödinger operators with point δ- and δ'- interactions on a sparse set are considered. Assuming that strengths of point interactions tend to ∞ we give simple sufficient conditions for such Schrödinger operators to have non-empty singular continuous spectrum and to have purely singular continuous spectrum, which coincides with R+.