A uniqueness criterion for ordinary differential equations
Consider the initial-value problem: \(x^{\prime}(t)=F(t,x(t))\), \(t\in [0,t_0]\), \(x(0)=x_0\). As a main result, the author shows that a convex combination of Nagumo- and Osgood-type growth conditions for the spatial variation of continuous functions ensures the uniqueness of the solution to the initial-value problem and the convergence of the successive approximations, defined by \(x_0 (t)=x_0\), \(t\in[0,T]\), \(x_{n+1} (t)=x_0 + \int_0^t F(s,x_n (s)) ds\), \(n>0\).
scientific article; zbMATH DE number 7615167
scientific article