Inverse spectral problem for Sturm-Liouville operator with discontinuous coefficient and cubic polynomials of spectral parameter in boundary condition

Advances in Difference Equations

Aynur l¹ 

[1] Department of Mathematics Education, Sinop University, Sinop, Turkey

关键词: inverse problem;    scattering data;    Sturm-Liouville operator;    spectral parameter;    discontinuous coefficient;    34A55;    34B40;    34B07;    34L25;    81U40;   

DOI  :  10.1186/s13662-015-0478-7

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, the inverse scattering problem for the Sturm-Liouville operator with discontinuous coefficient and cubic polynomials of the spectral parameter in the boundary condition is considered. The scattering data of the problem is defined, and its properties are investigated. The modified Marchenko main equation is obtained and it is shown that the potential is uniquely recovered by the scattering data.

【 授权许可】

CC BY