| Contents |
| We consider a class of scalar autonomous nonlinear integro-differential equations of the form
\[
(E) \ \ \ x'(t) = \int_0^1 v(s,x(t-s)) \ ds,
\]
where $v$ satisfies the negative feedback condition $v(s,u)u \leq 0$.
Our chief motivation is heuristic modeling of systems with state-dependent delay. We discuss some connections between $(E)$ and some previously studied differential delay equations. For a particular subclass of equations $(E)$, we formulate a non-increasing ``oscillation speed" for solutions, and show the existence of nontrivial slowly oscillating periodic solutions. |
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