Oscillation theory

In mathematics, in the field of ordinary differential equations, a nontrivial solution to an ordinary differential equation In mathematics, in the field of ordinary differential equations, a nontrivial solution to an ordinary differential equation is called oscillating if it has an infinite number of roots; otherwise it is called non-oscillating. The differential equation is called oscillating if it has an oscillating solution.The number of roots carries also information on the spectrum of associated boundary value problems.