Eigenvalues of a linear fourth-order differential operator with squared spectral parameter in a boundary condition (Q723814)

The boundary value problems which include the spectral parameter in one of the boundary conditions as a quadratic function arise in the acoustic wave guide problem and heat conduct problem. To this aim, in this paper, the authors study the spectrum and oscillation of eigenfunctions of a fourth-order BVP. They show that the eigenvalues are simple, form an infinitely increasing sequence without a finite accumulative point and satisfy some interlacing properties.