Oscillation theory

Summary

Oscillation theory studies the zeros of solutions of differential equations, above all of second-order linear equations $(p y')' + q y = 0$. Its main questions are whether solutions have infinitely many zeros, how the zeros are spaced, and how the zeros of different solutions are related. The theory started with the comparison and separation theorems of Charles Sturm. It gives criteria in terms of the coefficients, and it is linked to Sturm–Liouville theory, where the $n$-th eigenfunction has $n - 1$ zeros.