Oscillation (differential equation)

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In mathematics, in the field of ordinary differential equations, a non trivial solution to an ordinary differential equation

F(x,y,y',\ \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.

[edit] Examples

The differential equation

y'' + y = 0

is oscillating as sin(x) is a solution.

[edit] See also


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