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Abstract

Abstract:

In this paper, the authors discuss the half inverse problem for a quadratic pencil of the Schr\"{o}dinger operator on the finite interval [0, π]. Improving the Koyunbakan and Panakhov's method^[12], it is showed that if the potentials (q(x), p(x)) are prescribed on [π/2, π ], then only one spectrum is sufficient to determine the potentials (q(x), p(x)) on the interval [0, π/2) for the quadratic pencil of the Schr\"{o}dinger operator on the finite interval [0, π] and coefficient h of the boundary condition.

Key words: Quadratic pencil of the Schr\"{o}dinger operator, Boundary-value problem, Spectrum, Half inverse problem

CLC Number:

34A55

WANG Wu-Ping, YANG Chuan-Fu, HUANG Zhen-You. Half Inverse Problem for a Quadratic Pencil of |Schr\"{o}dinger Operators[J].Acta mathematica scientia,Series A, 2011, 31(6): 1708-1717.

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Half Inverse Problem for a Quadratic Pencil of |Schr\"{o}dinger Operators

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