Multiplicities and relative position of eigenvalues of a quadratic pencil of Sturm-Liouville operators (Q1585626)

The author considers the boundary value problem consisting of the equation \[ y''+ (\lambda^2- 2\lambda p(x)- q(x)) y=0,\quad x\in [0,\pi], \] and the boundary conditions \[ a_{i1}y(0)+ a_{i2} y'(0)+ a_{i3}y(\pi)+ a_{i4}y'(\pi)= 0,\quad i= 1,2. \] Criteria for the eigenvalues to be multiple are given and the relative position of the eigenvalues is studied.