Nonlinear Oscillations

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

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


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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© 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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