## Dispersions for linear differential equations of arbitrary order.(English)Zbl 0914.34010

The notion of dispersion $$\varphi (x)$$ for the linear differential equation $y''+p(x)y=0\tag{$$p$$}$ plays an important role in the Bor ůvka transformation theory of ($$p$$). The dispersion $$\varphi (x)$$ of ($$p$$) was introduced as the first right zero of a solution $$y(x)$$ vanishing at $$x_0$$. The notion of dispersion $$\varphi (x)$$ is generalized to certain classes of linear differential equations of arbitrary order. Relations between the asymptotic behaviour of solutions to these equations. The distribution of zeros of their solutions are investigated.

### MSC:

 34A30 Linear ordinary differential equations and systems 34C11 Growth and boundedness of solutions to ordinary differential equations 34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations 39B22 Functional equations for real functions
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