Oscillation and asymptotic behaviour of linear retarded differential equations of arbitrary order. (English) Zbl 0603.34066
The author derives conditions on p(t) and g(t) under which an nth order differential equation of the form \(x^{(n)}(t)\pm p(t)x[g(t)]=0,\) \(g(\infty)=\infty\) and \(t>g(t)\) is oscillatory or has other specific asymptotic behaviour for large t. The results are obtained by comparing solutions of the equations to related first and second order equations.
Reviewer: J.M.Cushing
MSC:
| 34K99 | Functional-differential equations (including equations with delayed, advanced or state-dependent argument) |
| 34K25 | Asymptotic theory of functional-differential equations |
| 34C10 | Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations |
