非线性Volterra积分微分方程的全局渐近稳定性

Global Asymptotic Stability of Nonlinear Volterra Integro-Differential Equation

利用不动点理论,研究非线性Volterra积分微分方程x′(t)=-a(t)x(t)+c(t)x′(t-τ1(t))+∫t t-τ2(t)k(t,s)g(t,x(s),x′(s))d s,给出方程在C 1空间上零解全局渐近稳定性的充分条件。这些新条件不需要中立项系数c和时滞τ1可微,也不要求时滞τ2二次可微且τ′2≠1,仅需要c,τ1,τ2连续,所得结论推广了已有文献中的相应结果,并给出了一个实例加以说明。

In this paper,the following nonlinear Volterra Integro-Differential equation x′(t)=-a(t)x(t)+c(t)x′(t-τ1(t))+∫t t-τ2(t)k(t,s)g(t,x(s),x′(s))d s was studied by using the fixed point theory.Sufficient conditions for global asymptotic stability of zero solution of the equation in C 1.These new conditions do not require the neutral term coefficient c and the delayτ1 differentiability,nor theτ2 quadratic differentiability andτ′2≠1,but only the continuity of c,τ1 andτ2.The conclusions generalize the corresponding results in the literature and give an example to illustrate them.