Oscillation (differential equation)

In mathematics, in the field of ordinary differential equations, a non trivial solution to an ordinary differential equation :$F(x,y,y\text{'},\; dots,\; y^\{(n-1)\})=y^\{(n)\}\; quad\; x\; in\; [0,+infty)$ 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.

Examples

The differential equation :$y"\; +\; y\; =\; 0$is oscillating as sin("x") is a solution.

See also

* Kneser theorem
* Sturm-Picone comparison theorem