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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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