Integral manifolds for semilinear evolution equations and admissibility of function spaces

  • Phi Hà Hanoi Univ. Education, Vietnam
  • Thiếu Huy Nguyễn Hanoi Univ. Sci. and Technology, Vietnam; Techn. Univ. Darmstadt, Germany
  • Thì Ngọc Hà Vụ Hanoi Univ. Sci. and Technology, Vietnam


We prove the existence of integral (stable, unstable, center) manifolds for the solutions to the semilinear integral equation $u(t) = U(t,s)u(s) + \int^t_s U(t,\xi)f (\xi,u(\xi))d\xi$ in the case where the evolution family $(U(t, s))_{t leq s}$ has an exponential trichotomy on a half-line or on the whole line, and the nonlinear forcing term $f$ satisfies the $\varphi $-Lipschitz conditions, i.e., $||f (t, x) — f (t, y) \leq \varphi p(t)||x — y||$, where $\varphi (t)$ belongs to some classes of admissible function spaces. Our main method invokes the Lyapunov-Perron methods, rescaling procedures, and the techniques of using the admissibility of function spaces.
How to Cite
Hà, P., T. H. Nguyễn, and T. N. H. Vụ. “Integral Manifolds for Semilinear Evolution Equations and Admissibility of Function Spaces”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 64, no. 6, June 2012, pp. 772-96,
Research articles