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oscillation theory : ウィキペディア英語版
oscillation theory
In mathematics, in the field of ordinary differential equations, a nontrivial solution to an ordinary differential equation
:F(x,y,y',\ \dots,\ y^)=y^ \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.
== Examples ==
The differential equation
:y'' + y = 0\
is oscillating as sin(''x'') is a solution.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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