Stability of a singular continuous spectrum of Sturm-Liouville operators

Abstract

We prove that there exists a continuous potentialq such that the operator generated by

$$(lu)(x) = - u^n (x) + \{ q(x) + \upsilon (x)\} u(x), 0 \leqslant (x)< \infty$$

and boundary conditionsu(0) cos α+u′(0) sin α=0 has a singular continuous spectrum in [0, 1] for every locally integrable functionv with compact support and every α ∈ [0, 2π].