abstr22
We provide a criterion for instability of equilibria of equations in the form x'(t) = g[(x')_t, x_t], which includes neutral delay equations with state-dependent delay.
The criterion is based on a lower bound Delta >0 for the delay in the neutral terms, on regularity assumptions of the functions in the equation, and on spectral assumptions on a semigroup used for approximation. The spectral conditions can be verified studying the associated characteristic equation. Estimates in the C^1-norm, a manifold containing the state space X_2 of the equation and another manifold contained in X_2, and an invariant cone method are used for the proof. We also give mostly self-contained proofs for the necessary prerequisites from the constant delay case, and conclude with an application to a mechanical example.