On Peano's theorem in Banach spaces

作者：Hajek Petr; Johanis Michal^*

来源：Journal of Differential Equations, 2010, 249(12): 3342-3351.

DOI：10.1016/j.jde.2010.09.013

• Peano's theorem
• Infinite-dimensional spaces

We show that if X is an infinite-dimensional separable Banach space (or more generally a Banach space with an infinite-dimensional separable quotient) then there is a continuous mapping f : X -> X such that the autonomous differential equation x' = f(x) has no solution at any point.

• 出版日期2010-12-15