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Multiple integral average conditions for oscillation of delay differential equations. (English) Zbl 0912.34061
The author considers delay differential equations of the form \[ x'(t)= \sum^n_{i=1} g_i(t)x(t- T_i(t))= 0,\tag{1} \] with \(g_i(t)\), \(T_i(t)\in C([t_0,\infty), [0,\infty))\), \(t- T(t)\to\infty\) and \(t- T_i(t)\to +\infty\) as \(t\to\infty\), \(i= 1,2,\dots,n\).
A method based on certain iterative processes is used to obtain some multiple integral average conditions for the oscillation of (1).

MSC:
34K11 Oscillation theory of functional-differential equations
34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations
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