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A differential equation without a solution

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Abstract

A direct construction is given of a functionf(x1, x2) ∈ C°, 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 functionf and all its derivatives vanish for x1=0.

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Literature cited

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Author information

Authors and Affiliations

  1. M. V. Lomonosov Moscow State University, USSR

    V. V. Grushin

Authors
  1. V. V. Grushin
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Additional information

Translated from Matematicheskie Zametki, Vol. 10, No. 2, pp. 125–128, August, 1971.

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Grushin, V.V. A differential equation without a solution. Mathematical Notes of the Academy of Sciences of the USSR 10, 499–501 (1971). https://doi.org/10.1007/BF01822870

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  • DOI: https://doi.org/10.1007/BF01822870

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