This article is cited in 9 papers

A differential equation without a solution

V. V. Grushin

M. V. Lomonosov Moscow State University

Abstract: A direct construction is given of a function $f(x_1, x_2)\in C^\infty$, such that the equation
$$ \frac{\partial u}{\partial x_1}+ix_1^{2k-1}\frac{\partial u}{\partial x_2}=f $$
has no solution in any neighborhood of the origin; the function $f$ and all its derivatives vanish for $x_1=0$.

UDC: 517.9

Received: 02.04.1970

 English version: Mathematical Notes, 1971, 10:2, 499–501

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