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Oscillation for solutions of nonlinear neutral differential equations with impulses. (English) Zbl 1005.34060

Summary: This paper is concerned with nonlinear neutral differential equations with impulses of the form \[ \left[x(t) -\sum^m_{i=1} P_i(t)x (t-\tau_i) \right]'+ Q(t)\prod^n_{j=1} \biggl|f_j\bigl(x(t-\sigma_j) \bigr)\biggr |^{\alpha_j} \text{sgn} x(t- \sigma_j)=0,\;t\geq t_0, \]
\[ x(t^+_k)= I_k\bigl(x (t_k)\bigr), \quad k=1,2, \dots. \] Some oscillation criteria for the solutions to this equation are established. An interesting example is given, that illustrates that impulses play an important role in giving rise to the oscillation of equations.

MSC:

34K11 Oscillation theory of functional-differential equations
34K45 Functional-differential equations with impulses
34K40 Neutral functional-differential equations
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