TITLE:
The Existence and Stability of Synchronizing Solution of Non-Autonomous Equations with Multiple Delays
AUTHORS:
Jinying Wei, Yongjun Li, Xiaohua Zhuo
KEYWORDS:
Pullback Attractor, Cocycle System, Stability, Synchronizing Solution
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.4 No.7,
July
25,
2016
ABSTRACT: In this paper, we consider an abstract non-autonomous
evolution equation with multiple delays in a Hilbert space H: u'(t) + Au(t) = F(u(t-r1),...,u((t-rn)) + g(t),where A: D(A)?H→His a positive definite selfadjoint operator, F: Hna→ His a nonlinear mapping, r1,...,rnare nonnegative constants, and g(t)∈ C(□;H)is bounded. Motivated by [1] [2], we obtain the existence and stability of
synchronizing solution under some convergence condition. By this result, we
provide a general approach for guaranteeing the existence and stability of
periodic, quasiperiodic or almost periodic solution of the equation.