Inverse problems of spectral analysis for the Sturm-Liouville operator   with regular boundary conditions
  We consider the Sturm-Liouville operator Lu=u''-q(x)u with regular but not strongly regular boundary conditions. Under some supplementary assumptions we prove that the set of potentials q(x) that ensure an asymptotically multiple spectrum is everywhere dense in the space of summable functions. 
Alexander Makin