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Abstract
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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

Ilkay Yaslan Karaca

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

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).