Sobre a não validade da forma fraca do Teorema de Peano em espaços de Banach com quociente separável de dimensão infinita

Abstract

In this present work, we study the “no validity” of Peano Theorem of Weak Form in Banach spaces with separable quotient of infinite dimension, in a more precise way, we show that if X is a Banach space with the quotient separable infinite-dimensional, then there is a continuous map f : X ! X such that autonomous differential equation x0 = f(x) has no solution at any point.