On the non-existence of <i>L</i>² solutions of a class of non-linear differential equations

Abstract

In 1950, Wintner ( 11 ) showed that if the function f ( x ) is continuous on the half-line [0, ∞) and, in a certain sense, is “ small when x is large ” then the differential equation does not have L 2 solutions, where the function y ( x ) satisfying (1) is called an L 2 solution if