Well-posedness of the Cauchy problem for nonlinear differential equations with variable delays
The authors consider the nonlinear delay differential equation \[ x'(t)=f(t,x(\tau_1(t)),\dots,x(\tau_j(t))), \] where \(x\in\mathbb R^n\), \(\tau_i(t)\leq t\), \(\tau_i'(t)> 0\), \(i =1,\dots,s\), and \(f\) satisfies certain boundedness and Lipschitz conditions. Under certain assumptions, the author proves that the solution depends continuously on the initial data and on small perturbations of the function \(f\).
scientific article; zbMATH DE number 2176620