The failure in computable analysis of a classical existence theorem for differential equations

Abstract

An example is given of a uniformly continuous constructive function f ( x , y ) f(x,y) with f ( 0 , 0 ) = 0 f(0,0) = 0 , such that the differential equation y ′ = f ( x , y ) y’ = f(x,y) with the initial condition y ( 0 ) = 0 y(0) = 0 has no constructive solution.