Kneser's theorem (differential equations)

In mathematics, the Kneser theorem can refer to two distinct theorems in the field of ordinary differential equations: the first one, named after Adolf Kneser, provides criteria to decide whether a differential equation is oscillating or not; the other one, named after Hellmuth Kneser, is about the topology of the set of all solutions of an initial value problem with continuous right hand side. == Statement of the theorem due to A. Kneser == Consider an ordinary linear homogeneous differential equation of the form y ″ + q ( x ) y = 0 {\displaystyle y''+q(x)y=0} with q : [ 0 , + ∞ ) → R {\displaystyle q:[0,+\infty )\to \mathbb {R} } continuous.

Source: Wikipedia — Kneser's theorem (differential equations) (CC BY-SA 4.0)

Kneser's theorem (differential equations)

In mathematics, the Kneser theorem can refer to two distinct theorems in the field of ordinary differential equations: the first one, named after Adolf Kneser, provides criteria to decide whether a differential equation is oscillating or not; the other one, named after Hellmuth Kneser, is about the topology of the set of all solutions of an initial value problem with continuous right hand side. == Statement of the theorem due to A. Kneser == Consider an ordinary linear homogeneous differential equation of the form y ″ + q ( x ) y = 0 {\displaystyle y''+q(x)y=0} with q : [ 0 , + ∞ ) → R {\displaystyle q:[0,+\infty )\to \mathbb {R} } continuous.

This neuron ends here.

Source: Wikipedia "Kneser's theorem (differential equations)" · CC BY-SA 4.0

Share this article: X · Bluesky
Privacy Policy