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Original Articles

Dual Equation and Inverse Problem for an Indefinite Sturm–Liouville Problem with m Turning Points of Even Order

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Pages 618-629 | Received 13 Sep 2011, Accepted 18 Sep 2012, Published online: 12 Nov 2012
 

Abstract

In this paper the differential equation y″ + (ρ 2 φ 2 (x) –q(x))y = 0 is considered on a finite interval I, say I = [0, 1], where q is a positive sufficiently smooth function and ρ 2 is a real parameter. Also, [0, 1] contains a finite number of zeros of φ 2 , the so called turning points, 0 < x 1 < x 2 < … < x m < 1. First we obtain the infinite product representation of the solution. The product representation, satisfies in the original equation. As a result the associated dual equation is derived and then we proceed with the solution of the inverse problem.

AMS Subject Classification:

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