Exponential Dichotomy and Stable Manifolds for Differential-Algebraic Equations on the Half-Line.

We study linear and semi-linear differential-algebraic equations (DAEs) on the half-line ℝ + . In our strategy, we first show a characterization for the existence of exponential dichotomy for linear DAEs based on the Lyapunov-Perron method. Then, we prove the existence of invariant stable manifolds for semi-linear DAEs in the case that the evolution family corresponding to a linear DAE admits an exponential dichotomy and the non-linear forcing function fulfills the non-uniform φ-Lipschitz condition where the Lipschitz function φ belongs to wide classes of admissible function spaces such as Lp, 1 ≤ p ≤ ∞ , and Lp,q. [ABSTRACT FROM AUTHOR]