Asymptotic behavior for differences of eigenvalues of two Sturm-Liouville problems with smooth potentials (Q629226)

The paper deals with two Sturm-Liouville problems for the ordinary differential operators defined by \[ D(L)=\{u \in H^2(0,\pi): u^{\prime}(0)=0, u^{\prime}(\pi)+hu(\pi)=0\}, \] \[ Ly=-y^{\prime \prime}+q(x)y \quad \forall \; y \in D(L) \] and by two different potentials \(q\). The asymptotics for the differences of the square roots of the eigenvalues is given.