NONLOCAL PROBLEM FOR A EQUATION OF MIXED TYPE OF THIRD ORDER WITH MULTIPLE CHARACTERISTICS
This article is devoted to research of the unique solvability of a nonlocal problem with fractional derivatives in the boundary condition for equations of mixed type of third order with multiple characteristics. When neravenstvennogo restrictions on the type of function known uniqueness theorem. The proof is carried out by energy integrals. In the proof of the uniqueness of the solution of the problem set the effect of the ratio of the lowest (50) derivative in the equation on the unique solvability of the boundary value problem. To prove the existence of a solution of the problem, obtained the relationship between the trace of the unknown function u(x,0)=(x) and the following derivatives of the unknown function uy(x, 0)=v(x) brought to the line of degeneracy y=0 of hyperbolic and parabolic part of the mixed area. The method of solving the problem of the existence of the Tricomi redutsirovanno equivalent to the Fredholm integral equation of the second kind (100), with respect to the following derivative of the unknown function, which should be unconditional solvability of the uniqueness of the solution of the problem.