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''interval of disconjugacy''

A connected interval  $  J $
on the real axis  $  \mathbf R $
such that any non-trivial solution  $  x = x ( t) $
of a given ordinary linear differential equation of order  $  n $
with real coefficients,

$$ \tag{* }
x  ^ {(} n) + a _ {1} ( t) x  ^ {(} n- 1) + \dots + a _ {n} ( t) x
 =  0 ,
$$

has on it more than  $  n- 1 $
zeros, an  $  m $-
fold zero counted  $  m $
times. Properties of solutions of (*) on a non-oscillation interval have been well studied (see, for example, [[#References|[1]]]–[[#References|[3]]]). There are several generalizations of the concept of a non-oscillation interval, to linear systems of differential equations, to non-linear differential equations, and also to other types of equations (difference, with deviating argument).

====References====
<table><TR><TD valign="top">[1]</TD> <TD valign="top">  P. Hartman,   "Ordinary differential equations" , Birkhäuser  (1982)</TD></TR><TR><TD valign="top">[2]</TD> <TD valign="top">  A.Yu. Levin,   "Non-oscillation of solutions of the equation <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/n/n067/n067220/n0672209.png" />"  ''Russian Math. Surveys'' , '''24''' :  2  (1969)  pp. 43–99  ''Uspekhi Mat. Nauk'' , '''24''' :  2  (1969)  pp. 43–96</TD></TR><TR><TD valign="top">[3]</TD> <TD valign="top">  W.A. Coppel,   "Disconjugacy" , Springer  (1971)</TD></TR></table>