TY - JOUR
AU - Trinh Xuan Yen,
PY - 2022/09/30
Y2 - 2024/07/25
TI - INVARIANT CENTER - UNSTABLE MANIFOLDS FOR PARTIAL FUNCTIONAL DELAY DIFFERENTIAL EQUATIONS
JF - UTEHY Journal of Science and Technology
JA - jst
VL - 35
IS -
SE - Articles
DO -
UR - https://tapchi.utehy.edu.vn/index.php/jst/article/view/561
SP - 84-89
AB - We prove the existence of an invariant center-unstable manifold of -class for solutions to the partial functional delay differential equation of the formu'(t) = A(t)u(t) + f(t, ut), t∈Rwhen its linear part, the family operators (A(t))t ∈R, generates the evolution family (U(t,s))t ≥ s having an exponential dichotomy or trichotomy on the R and the nonlinear forcing delay term f satisfies the -Lipschitz condition, i.e., ‖f(t,ut) − f(t,vt)‖C ≤ ‖ut − vt‖ where ut, vt∈:= C([−r,0],X), and belongs to an admissible function space on R. Our main methods invoke Lyapunov-Perron methods and use admissible function sapces.
ER -