The distance between points of a solution of a second order linear differential equation satisfying general boundary conditions
Summary: This paper presents a method to obtain lower and upper bounds for the minimum distance between points \(a\) and \(b\) of the solution of the second order linear differential equation \(y'' + q(x) y = 0\) satisfying general separated boundary conditions of the type \(a_{11} y(a) + a_{12} y'(a) = 0\) and \(a_{21} y(b) + a_{22} y'(b) = 0\). The method is based on the recursive application of a linear operator to certain functions, a recursive application that makes these bounds converge to the exact distance between \(a\) and \(b\) as the recursivity index grows. The method covers conjugacy and disfocality as particular cases.
scientific article; zbMATH DE number 7021761
scientific article