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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 a11y(a)+a12y′(a)=0 and a21y(b)+a22y′(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.

The Distance between Points of a Solution of a Second Order Linear Differential Equation Satisfying General Boundary Conditions