Analyticity of Bounded Solutions of Analytic State-Dependent Delay Differential Equations

We study the analyticity of bounded solutions of systems of analytic state-dependent delay differential equations. We obtain the analyticity of solutions by transforming the system of state-dependent delay equations into an abstract ordinary differential equation in a subspace of the sequence space $l^{\mathrm{\infty }}({\mathbb{R}}^{N+1})$ and prove the existence of complex extension of the bounded solutions. An example is given to illustrate the general results.