求解一类不连续的Sturm-Liouville问题

his paper investigate a class of discontinuous Sturm-Liouville problems with eigenparameter dependent boundary conditions. A self-adjoint linear operator $A$ is defined in a suitable Hilbert space such that the eigenvalues of such a problem coincide with those of $A$. We prove that the eigenvalues of the problem are analytically simple. Based on these, we demonstrate some approximate solutions of eigenvalues and eigenfunctions for a given problem.