Oscillation theory

In mathematics, in the field of ordinary differential equations, a nontrivial solution to an ordinary differential equation F ( x , y , y ′ , … , y ( n − 1 ) ) = y ( n ) x ∈ [ 0 , + ∞ ) {\displaystyle 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.

From Wikipedia

In mathematics, in the field of ordinary differential equations, a nontrivial solution to an ordinary differential equation F ( x , y , y ′ , … , y ( n − 1 ) ) = y ( n ) x ∈ [ 0 , + ∞ ) {\displaystyle 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. The number of roots carries also information on the spectrum of associated boundary value problems.

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