Uniqueness of the potential function for the vectorial Sturm-Liouville equation on a finite interval
1 Department of Mathematics, Tamkang University, No.151, Yingzhuan Rd., Danshui Dist., New Taipei City 25137, Taiwan, PR China
2 Department of Electronic Engineering, China University of Science and Technology, No.245, Academia Rd., Sec. 3, Nangang District, Taipei City 115, Taiwan, PR China
Citation and License
Boundary Value Problems 2011, 2011:40 doi:10.1186/1687-2770-2011-40Published: 26 October 2011
In this paper, the vectorial Sturm-Liouville operator is considered, where Q(x) is an integrable m × m matrix-valued function defined on the interval [0,π] The authors prove that m2+1 characteristic functions can determine the potential function of a vectorial Sturm-Liouville operator uniquely. In particular, if Q(x) is real symmetric, then characteristic functions can determine the potential function uniquely. Moreover, if only the spectral data of self-adjoint problems are considered, then m2 + 1 spectral data can determine Q(x) uniquely.