Continuation results for differential equations without uniqueness by two Liapunov functions
The author considers a system of nonlinear ordinary differential equations written as follows: (1) \(x'=f(t,x,y)\), \(y'=g(t,x,y)\), where x and y are vectors of n and m dimensions, respectively, while f and g are continuous functions on \([0,\infty)\times {\mathbb{R}}^ n\times R^ m\). His aim is to give some sufficient conditions under which every solution to (1) is continuable on \([t_ 0,\infty)\) for every \(t_ 0\geq 0\) (existence in the future). The results are phrased in the form of two long theorems and constitute an extention of some earlier results due to the author on non-unique systems.
scientific article; zbMATH DE number 3906882