A generalized Picard-Lindelof theorem

作者：Siegmund Stefan^*; Nowak Christine; Diblik Josef

来源：Electronic Journal of Qualitative Theory of Differential Equations, 2016, (28): 28.

DOI：10.14232/ejqtde.2016.1.28

• Picard-Lindelof theorem
• initial value problem
• generalized Lipschitz condition
• unique solvability

We generalize the Picard-Lindelof theorem on the unique solvability of initial value problems (x) over dot = f (t, x), x (t(0)) = x(0), by replacing the sufficient classical Lipschitz condition of f with respect to x with a more general Lipschitz condition along hyperspaces of the (t, x)-space. A comparison with known results is provided and the generality of the new criterion is shown by an example.

• 出版日期2016