Spectral asymptotics and a trace formula for a fourth-order differential operator corresponding to thin film equation (Q6109727)

In the paper, the high-energy asymptotics of the eigenvalues and a trace formula are found for a self-adjoint fourth-order operator on the interval with Neumann-Dirichlet boundary conditions and periodic coefficients. The operator considered here acts as \[ H y = y^{(4)}+(py')'+qy \] on \(L^2(0,1)\) with the boundary conditions \[ y'(0) = y'''(0)+p(0) y'(0) = y(1) = y''(1) = 0 \] and a certain domain (for brevity, we do not state it here explicitly). The coefficients \(p\) and \(q\) are 1-periodic. This operator is connected with the one-dimensional thin film equation.