On existence and uniqueness of solutions of the Dirichlet's problem for pseudodifferential elliptic equations in domains with non-compact boundaries

It is found a class of uniqueness of solutions of the Dirichlet's problem for pseudodifferential elliptic equations in domains with non-compact boundaries. The restriction on a growth of solutions is formulated in terms of geometric characteristics of unbounded domain $\Omega$. They were introduced earlier in author's papers for quasielliptic equations. It is proved the existence of solution belonging to the class of uniqueness.