Solvability theorems for an inverse nonself-adjoint Sturm-Liouville problem with nonseparated boundary conditions
Let \(\{\lambda_k\}\) be the eigenvalues of the boundary value problem \[ -y''+q(x)y=\lambda y, \] \[ y'(0)+a_{11}y(0)+a_{12}y(\pi)=y'(\pi)+a_{21}y(0)+a_{22}y(\pi)=0. \] The following inverse problem is solved: given three eigenvalues \(\lambda_1, \lambda_2, \lambda_3\), construct three coefficients \(a_{12}, a_{21}, a_{22}\), provided the function \(q(x)\) and the coefficient \(a_{11}\) are known a priori.
scientific article; zbMATH DE number 6485725
scientific article