International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 25, Pages 1599-1614

On Hill's equation with a discontinuous coefficient

Ilkay Yaslan Karaca

Department of Mathematics, Faculty of Science, Ege University, Izmir 35100, Turkey

Received 25 February 2002

Copyright © 2003 Ilkay Yaslan Karaca. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We research the asymptotic formula for the lengths of the instability intervals of the Hill's equation with coefficients q(x) and r(x), where q(x) is piecewise continuous and r(x) has a piecewise continuous second derivative in open intervals (0,b) and (b,a)(0<b<a).