ABSTRACT
Let us note that in the "limiting" case f3 = /3c, the equations (6) and (8) are solved by >'0 = 0 provided d � 3, so that the function 1/;0 is well defined by (7) , (10). However, it turns out that 1/;0 does not belong to Z2(Zd) for d = 3 and d = 4, because the function 1/( -¢) is not square integrable (see (7) ) . Hence, for f3 = f3c the operator H has the eigenvalue >'0 = 0 ( "sticking" to the upper edge of the essential spectrum) only in higher dimensions, d � 5. This remark enlightens the additional bifurcation in the critical point f3 = f3c with respect to the space dimension (see Theorem l(b) below).
