The inverse problem for differential pencils with eigenparameter dependent boundary conditions from interior spectral data

Abstract

In this paper, we discuss the inverse problem for differential pencils with eigenparameter dependent boundary conditions on the finite interval [ 0 , π ] from interior spectral data and show that if coefficients h j ( j = 0 , 1 ) of the boundary condition are given, then potentials ( q ( x ) , p ( x ) ) and coefficients H j ( j = 0 , 1 ) of the boundary condition can be uniquely determined by a set of values of eigenfunctions at some interior point and parts of two spectra.