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(P1) consists of periodically extended delta-distributions, (P2) of periodic step potentials and (P3) contains certain periodic potentials $V,q\\in H^r_{\\per}(\\R)$ for $r\\in [1,3/2)$. Among other assumptions we suppose that $|f(x,s)|\\leq c(1+ |s|^p)$ for some $c>0$ and $p>1$. 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