Distribution of eigenvalues for the discontinuous boundary-value problem with functional-manypoint conditions (Q1601471)

The authors consider the problem \(ay''+cy=\lambda ^2 y\) on \([-1,0)\cup (0,1]\), where \(a\) and \(c\) are complex-valued functions, with four functional-multipoint boundary conditions. These conditions involve not only the values of \(y\) and \(y'\) at \(-1, -0, +0, 1\) and various internal points, but also certain abstract linear functionals. Sufficient conditions are derived for the existence of an infinite number of eigenvalues, and asymptotic formulae for the eigenvalues are given.