On Bounds of Eigenvalues of Complex Sturm-Liouville Boundary Value Problems

Abstract

The paper is concerned with eigenvalues of complex Sturm-Liouville boundary value problems. Lower bounds on the real parts of all eigenvalues are given in terms of the coefficients of the corresponding equation and the bound on the imaginary part of each eigenvalue is obtained in terms of the coefficients of this equation and the real part of the eigenvalue.

Estimates on the eigenvalues of complex nonlocal Sturm-Liouville problems

“…Recently, the estimates on the upper bound have been solved for the local indefinite Sturm-Liouville problem, i.e., K(x, t) = 0, w changes its sign on [0, 1] in (1.1) with self-adjoint boundary conditions in [14,21,31]. The estimates on the bounds of eigenvalues for the complex local Sturm-Liouville problems have been studied by the Rayleigh-Ritz method for w ≡ 1, q > 0 in [11] and for the general case in [12].…”