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On equations with delay depending on solution. (English) Zbl 1012.34066
The authors study the equation $$\dot x(t) +\sum_{i=1}^m A_i(t) x(t-(H_ix)(t))=f(t)$$ in $$\mathbb{R}^n$$ where $$A_i$$ and $$f$$ are measurable and essentially bounded functions and the $$H_i$$ are scalar-valued measurable functions. The presence of the state-dependent time lag $$H_ix$$ makes the equation nonlinear. Investigating the corresponding linear equations, sufficient conditions are obtained for the boundedness, oscillation and nonoscillation of the solutions.

##### MSC:
 34K11 Oscillation theory of functional-differential equations 34K12 Growth, boundedness, comparison of solutions to functional-differential equations 34K10 Boundary value problems for functional-differential equations
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