2019
Том 71
№ 11

All Issues

On trivial differential equations in the spaces $L_p,\; 0 < p < 1$

Popova L. V.

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Abstract

A description of the set $X_p$ of all solutions of the trivial Cauchy problem in $L_p, o< p <1$, 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 $p$ and emanate from O relative to the $p$-norm, which is equal to the minimal constant in the Hölder condition.

English version (Springer): Ukrainian Mathematical Journal 44 (1992), no. 9, pp 1132-1135.

Citation Example: Popova L. V. On trivial differential equations in the spaces $L_p,\; 0 < p < 1$ // Ukr. Mat. Zh. - 1992. - 44, № 9. - pp. 1238–1242.

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