We study some spectral problems for a second-order differential operator with periodic potential. Notice that the given potential is a sum of zero- and first-order generalized functions. It is shown that the spectrum of the investigated operator consists of infinite number of gaps whose length limit unlike the classic case tends to nonzero constant in some place and to infinity in other place.
"Spectrum of a Differential Operator with Periodic Generalized Potential." Abstr. Appl. Anal. 2007 1 - 8, 2007. https://doi.org/10.1155/2007/74595