Counting and computing eigenvalues of left-definite Sturm–Liouville problems

摘要

For left-definite regular self-adjoint Sturm–Liouville problems we construct a function N(λ) which counts the number of positive eigenvalues less than λ when λ is positive and the number of negative eigenvalues greater than λ when λ is negative. Based on this function we construct a code for the numerical computation of the eigenvalues and illustrate its use with examples. The boundary conditions can be separated or coupled.The code is available from www.mcs.le.ac.uk/~mmarletta/programs.html.