Instability intervals of a Hill's equation with piecewise constant and alternating coefficient

In this paper, we obtain asymptotic formulas for eigenvalues of the periodic and the semiperiodic boundary value problems associated with a Hill's equation having piecewise constant and alternating coefficient. As a corollary, it is shown that the lengths of instability intervals of the considered Hill's equation tend to infinity. (C) 2004 Elsevier Ltd. All rights reserved.