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-r<sub>1</sub><sub></sub>),...,u((t-r<sub&g...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-r<sub>1</sub><sub></sub>),...,u((t-r<sub>n</sub><sub></sub>)) + g(t), where A: D(A)?H→H is a positive definite selfadjoint operator, F: H<sup>n</sup><sub>a</sub> → H is a nonlinear mapping, r<sub>1</sub>,...,r<sub>n</sub> are 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.展开更多
文摘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-r<sub>1</sub><sub></sub>),...,u((t-r<sub>n</sub><sub></sub>)) + g(t), where A: D(A)?H→H is a positive definite selfadjoint operator, F: H<sup>n</sup><sub>a</sub> → H is a nonlinear mapping, r<sub>1</sub>,...,r<sub>n</sub> are 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.
