Among the eigenvalue problems of the Laplacian, the biharmonic operator eigenvalue problems are interesting projects because these problems root in physics and geometric analysis. The buckling problem is one of the most important problems in physics, and many studies have been done by the researchers about the solution and the estimate of its eigenvalue. In this paper, first, we obtain the evol...

A comprehensive survey of some recent results regarding parameterized inverse eigenvalue problems is given in this paper. Speciic topics include: additive and multiplicative inverse eigenvalue problems, classical inverse eigenvalue problems and generalized inverse eigenvalue problems. Both the theoretic and algorithmic aspects are reviewed. Some open problems are revealed to stimulate further r...

The construction of matrices with prescribed eigenvalues is a kind inverse eigenvalue problems. authors proposed an algorithm for constructing band oscillatory based on the extended discrete hungry Toda equation (Numer. Algor. 75:1079--1101, 2017). In this paper, we develop new generalization equation. improves previous so that one can produce more generic than in certain sense. We compare by n...

The investigation of the far field operator and the Factorization Method in inverse scattering theory leads naturally to the study of corresponding interior transmission eigenvalue problems. In contrast to the classical Dirichletor Neumann eigenvalue problem for −∆ in bounded domains these interior transmiision eigenvalue problem fail to be selfadjoint. In general, existence of eigenvalues is a...