We investigate the global existence of solutions and stability of zero solution for the functional differential equation with impulses:dxdt=f(t,x t),t≥ t 0, △ x=x(t)-x(t -)=I k(x(t -)),t=t k, k∈ N;where ...We investigate the global existence of solutions and stability of zero solution for the functional differential equation with impulses:dxdt=f(t,x t),t≥ t 0, △ x=x(t)-x(t -)=I k(x(t -)),t=t k, k∈ N;where x t(θ)=x(t+θ), -τ≤ θ≤ 0, I k(x)∈ C(R n,R n), lim k→∞ t k=+∞ and satisfiest 0<t 1<t 2<…<t n<….We have got a criterion about the global existence and a comparative theorem of stability between the given impulsive functional differential equation and an impulsive ordinary differential equation.展开更多
文摘We investigate the global existence of solutions and stability of zero solution for the functional differential equation with impulses:dxdt=f(t,x t),t≥ t 0, △ x=x(t)-x(t -)=I k(x(t -)),t=t k, k∈ N;where x t(θ)=x(t+θ), -τ≤ θ≤ 0, I k(x)∈ C(R n,R n), lim k→∞ t k=+∞ and satisfiest 0<t 1<t 2<…<t n<….We have got a criterion about the global existence and a comparative theorem of stability between the given impulsive functional differential equation and an impulsive ordinary differential equation.
