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On Goursat and Dirichlet problems for one equation of the third order

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Nonlinear Oscillations

We study the problem of the unique solvability of Goursat and Dirichlet problems for one partial differential equation of the third order. We construct a Riemann function for a linear third-order equation with a hyperbolic operator in the principal part, study some properties of the Riemann function, and then use them to prove theorems on the existence and uniqueness of a solution of the problems indicated.

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Authors and Affiliations

  1. Institute of Mathematics, Uzbekistan Academy of Sciences, Tashkent, Uzbekistan

    T. D. Dzhuraev

  2. Uzbekistan National University, Tashkent, Uzbekistan

    T. D. Dzhuraev & O. S. Zikirov

Authors
  1. T. D. Dzhuraev
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  2. O. S. Zikirov
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Correspondence to O. S. Zikirov.

Additional information

Translated from Neliniini Kolyvannya, Vol. 11, No. 3, pp. 305–315, July–September, 2008.

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Dzhuraev, T.D., Zikirov, O.S. On Goursat and Dirichlet problems for one equation of the third order. Nonlinear Oscill 11, 320–330 (2008). https://doi.org/10.1007/s11072-009-0033-0

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  • DOI: https://doi.org/10.1007/s11072-009-0033-0

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