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Dual equation and inverse problem for an indefinite Sturm–Liouville problem with m turning points of even order

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.

Keyword : turning point, Sturm–Liouville problem, indefinite problem, dual equation, inverse problem

How to Cite
Marasi, H., & Akbarfam, A. J. (2012). Dual equation and inverse problem for an indefinite Sturm–Liouville problem with m turning points of even order. Mathematical Modelling and Analysis, 17(5), 618-629. https://doi.org/10.3846/13926292.2012.732972
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Nov 1, 2012
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