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