KNESER THEOREM

In mathematics, in the field of ordinary differential equations, the 'Kneser theorem', named after Adolf Kneser, provides criteria to decide whether a differential equation is oscillating or not.

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Kneser theorem

Kneser theorem

Given an ordinary linear homogenous differential equation of the form
:$-y\text{'}\text{'}\; +\; q(x)y\; =\; 0$
with
:$q:\; [0,+infty]\; o\; mathbb\{R\}$
continuous and ''q''(''x'') > 0, then the equation is non-oscillating if
:
and oscillating if
:
We recall, that the equation is oscillating, if $y$ has an infinite number of zeros and non-oscillating otherwise.