The uniqueness theorem for boundary value problem with aftereffect and eigenvalue in the boundary condition (Q2892570)

The boundary value problem NEWLINE\[NEWLINEly(x):=-y^{\prime \prime}(x)+q(x)y(x)+\int_0^x M(x-t)y(t)dt = \lambda^2 y(x),\, NEWLINE\]NEWLINE NEWLINE\[NEWLINEy(0)=0, \qquad ay^{\prime}(\pi,\lambda) + \lambda y(\pi, \lambda)=0NEWLINE\]NEWLINE with ``aftereffect'' on finite interval \( 0<x<\pi\) is studied, \(\lambda\) is the spectral parameter, \(q \in L_2(0,\pi).\) \(a \neq 0\) is real parameter. The authors prove that the function \(M\) and the constant \(a\) are uniquely determined from a dense set of model points and given \(q\).