A partial inverse problem for the differential pencil on a star-shaped graph
The paper deals with the quadratic differential pencil on a star-shaped graph: \[ -y_j''(x_j)+q(x_j) y_j(x_j)+2\lambda p_j(x_j) y_j(x_j)=\lambda^2 y_j(x_j) \] on each edge \(e_j\), \(j = \overline{1, m}\), with standard matching conditions in the internal vertex and with the boundary conditions, depending on the spectral parameter. The so-called partial inverse problems is studied, which consist in recovering the functions \(p_1\), \(q_1\), using a part of the spectrum, while the coefficients on the other edges \(e_j\), \(j = \overline{2, m}\), are known a priori. It is supposed that the given eigenvalues do not coincide with the eigenvalues of the pencils, associated with separate edges. The main results of the paper are the uniqueness theorem for the solution of the inverse problem, and a constructive procedure for solving this problem.
scientific article; zbMATH DE number 6832352
scientific article