In this paper the eigenvalues of the periodic and the semi-periodic boundary value problems associated with Hill's equation are investigated in the case of piecewise constant coefficient. As a corollary the asymptotic formula for the lengths of the instability intervals of Hill's equation is derived and it is shown that they increase beyond all bounds. Also, the conditions for coexistence of periodic and semi-periodic solutions are indicated.
YASLAN, I. and GUSEINOV, G.Sh. (1997) "On Hill's Equation with Piecewise Constant Coefficient," Turkish Journal of Mathematics: Vol. 21: No. 4, Article 9. Available at: https://journals.tubitak.gov.tr/math/vol21/iss4/9