AbstractA spectral boundary problem on the eigenfield of an inflated/deflated
stretched circular membrane, which is clamped to a circular cylindrical cavity filled with
a liquid, is examined. The paper presents an operator formulation of the problem and
proposes a new semi-analytical approximate method. The method captures singular
behavior of the solution in the pole and at the fastening contour of the membrane.
In this paper, we investigate a class of discontinuous singular Sturm-Liouville problems with limit circle endpoints and eigenparameter dependent boundary conditions. Operator formulation is constructed and asymptotic formulas for eigenvalues and fundamental solutions are given. Moreover, the completeness of eigenfunctions is discussed.