Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4590986 | Journal of Functional Analysis | 2011 | 16 Pages |
Abstract
In this paper, we discuss the existence and asymptotic stability of the time periodic solution for the evolution equation with multiple delays in a Hilbert space Hu′(t)+Au(t)=F(t,u(t),u(t−τ1),…,u(t−τn)),t∈R, where A:D(A)⊂H→HA:D(A)⊂H→H is a positive definite selfadjoint operator, F:R×Hn+1→HF:R×Hn+1→H is a nonlinear mapping which is ω-periodic in t , and τ1,τ2,…,τnτ1,τ2,…,τn are positive constants. We present essential conditions on the nonlinearity F to guarantee that the equation has ω-periodic solutions or an asymptotically stable ω-periodic solution. The discussion is based on analytic semigroups theory and an integral inequality with delays.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Yongxiang Li,