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

Neuman, František

Arch. Math., Brno 33, No. 1-2, 147-155 (1997).

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.

Reviewer: J.Vosmanský (Brno)

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

Keywords:

linear differential equations; distribution of zeros; asymptotic behaviour; Abel’s functional equation