On Peano's theorem in Banach spaces

[摘要] 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. (C) 2010 Elsevier Inc. All rights reserved.

[发布日期] 2010-12-15

[关键词] Peano's theorem;Infinite-dimensional spaces