On some nonlocal problems for third order equations with multiple characteristics
We consider two boundary value problems for an equation of the third order with multiple characteristics and a nonlocal condition in time. In order to prove uniqueness, we use the method of energy integrals. By the method of potentials, the Green’s function is constructed and employed to prove the unique solvability of the problems in question. The inﬂuence is studied of the boundary conditions on smoothness of solutions.