Integral manifolds for semilinear evolution equations and admissibility of function spaces - Vu Thi Ngoc Ha; Nguyen Thieu Huy; Ha Phi (Український математичний журнал, 2012)
We prove the existence of integral (stable, unstable, and center) manifolds for the solutions to a semilinear integral equation in the case where the evolution family (U(t, s)) t≥s has an exponential trichotomy on a half line or on the whole line, and the nonlinear forcing term f satisfies the φ-Lipschitz conditions, i.e., where φ(t) belongs to some classes of admissible function spaces. Our main method is based on the Lyapunov–Perron methods, rescaling procedures, and the techniques of using the admissibility of function spaces.