Nonlinear Oscillations

, Volume 11, Issue 3, pp 320–330 | Cite as

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

  • T. D. Dzhuraev
  • O. S. Zikirov

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.


Dirichlet Problem Principal Part Unique Solvability Homogeneous Boundary Condition Riemann Function 
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Copyright information

© Springer Science+Business Media, Inc. 2008

Authors and Affiliations

  1. 1.Institute of MathematicsUzbekistan Academy of SciencesTashkentUzbekistan
  2. 2.Uzbekistan National UniversityTashkentUzbekistan

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