Trivial differential equations in spaces $L_p, 0 < p< 1$

Abstract

A description of the set $X_p$  of all solutions of the trivial Cauchy problem in $L_p, 0 < p< 1$ is presented. The principal result is Theorem 2, which asserts that $X_p$ is a closed subspace of the $p$ -Banach space $H_p$ of all curves in $L_p$ that satisfy a Hölder condition of order $р$  and emanate from relative to the $p$ -norm, which is equal to the minimal constant in the Hölder condition.