Spectrum of discrete second-order Neumann boundary value problems with sign-changing weight
Summary: We study the spectrum structure of discrete second-order Neumann boundary value problems (NBVPs) with sign-changing weight. We apply the properties of characteristic determinant of the NBVPs to show that the spectrum consists of real and simple eigenvalues; the number of positive eigenvalues is equal to the number of positive elements in the weight function, and the number of negative eigenvalues is equal to the number of negative elements in the weight function. We also show that the eigenfunction corresponding to the \(j\)th positive/negative eigenvalue changes its sign exactly \(j-1\) times.
discrete second-order Neumann boundary value problems
scientific article; zbMATH DE number 6306598
scientific article