A global stability criterion in nonautonomous delay differential equations
- Muroya, Yoshiaki
DOIAbstract
AbstractConsider the following nonautonomous nonlinear delay differential equation:{dy(t)dt=−a(t)y(t)−∑i=0mai(t)gi(y(τi(t))),t⩾t0,y(t)=ϕ(t),t⩽t0, where we assume that there is a strictly monotone increasing function f(x) on (−∞,+∞) such that{f(0)=0,0<gi(x)f(x)⩽1,x≠0,0⩽i⩽m,andiff(x)≢x,thenlimx→−∞f(x)orlimx→+∞f(x)is finite. In this paper, to the above nonautonomous nonlinear delay differential equation, we establish conditions of global asymptotic stability for the zero solution. In particular, for a special wide class of f(x) which contains two cases f(x)=ex−1 and f(x)=x, we give more explicit conditions which are some extension of the “3/2-type criterion.” Applying these to discrete models of nonautonomous delay differential equations, we a...
Add to ORKG