We prove the existence of integral (stable, unstable, center) manifolds of admissible classes for the solutions to the semilinear integral equation when the evolution family has an exponential trichotomy on a half-line or on the whole line, and the nonlinear forcing term f satisfies the (local or global) φ-Lipschitz conditions, i.e., ||f(t,x)-f(t,y)|| ≤ φ(t)||x-y|| where φ(t) belongs to some classes of admissible function spaces. These manifolds are formed by trajectories of the solutions belonging to admissible function spaces which contain wide classes of function spaces like function spaces of type, the Lorentz spaces and many other function spaces occurring in interpolation theory. Our main methods involve the Lyapunov-Perron method, rescaling procedures, and techniques using the admissibility of function spaces.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap112-2-3,
author = {Nguyen Thieu Huy and Vu Thi Ngoc Ha},
title = {Admissibly integral manifolds for semilinear evolution equations},
journal = {Annales Polonici Mathematici},
volume = {111},
year = {2014},
pages = {127-163},
zbl = {1315.34049},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap112-2-3}
}
Nguyen Thieu Huy; Vu Thi Ngoc Ha. Admissibly integral manifolds for semilinear evolution equations. Annales Polonici Mathematici, Tome 111 (2014) pp. 127-163. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap112-2-3/