Exponential stability and inequalities of solutions of abstract functional differential equations

[摘要] With the Lyapunov second method, we study the abstract functional differential equation, du/dt = f(t, u(t)). We obtain inequalities of solutions and exponential stability with conditions like: (i) W-1(|u(t)|(X)) <= V(t,u(t)) <= W-2(D(t,u(t)))+integral L-t(t-h)(s)W-1(vertical bar u(s)vertical bar(X)) ds, (ii) V'(t, u(t)) <= -eta(t)W-2(D(t,u(t))) + P(t). Applications in ordinary and partial functional differential equations are given. (c) 2006 Elsevier Inc. All rights reserved.

[发布日期] 2006-12-15

[关键词] Lyapunov second method;exponential asymptotic stability;inequalities of solutions;abstract functional differential equations