Spectral asymptotics for two-term even-order differential operators with homogeneous delay

Abstract

We consider two-term even-order operators on the unit interval with homogeneous delay and with Dirichlet and Neumann boundary conditions. The main result provides to the eigenvalue asymptotics of this operator with respect to all indices enumerating the eigenvalues. This asymptotic formula is uniform in the parameter of the homogeneous delay. We also discuss the nontrivial high-frequency phenomenon demonstrated by the uniform spectral asymptotics.