International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 25, Pages 1599-1614
doi:10.1155/S016117120320209X
On Hill's equation with a discontinuous coefficient
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.
Abstract
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).