On solvability of nonlocal problem for third-order equation

In this paper nonlocal problem with integral conditions for partial differential equation of the third order is considered. The existence of a unique classical solution is proved in rectangular domain. The proof is carried out by the method of auxiliary problems. At first the problem for a new function for partial differential equation of the first order is considered. Then the solvability of integral analogue of Goursat problem for hyperbolic equation of the second order is proved by equivalent reduction of the problem to the Volterra integral equation of the second kind.