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Attractors for differential equations with unbounded delays. (English) Zbl 1135.34040
For some differential equations with infinite delay (e.g., of logistic or Volterra-Lotka-type), boundedness properties of the solutions are proved; such as compact attractors, absorbing sets, and pullback attractors in the non-autonomous case. The paper starts with a section that includes a set-valued context. The main techniques are assumptions on the nonlinearity like \quad $<F(x), x> \; \leq\; - \text{const}\cdot \vert \vert x\vert \vert ^2$, Gronwall type estimates, and the Arzelà-Ascoli theorem.

MSC:
 34K25 Asymptotic theory of functional-differential equations 37L30 Attractors and their dimensions, Lyapunov exponents
Full Text:
References:
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