On the completeness of a system of decreasing elementary solutions for one class of fourth-order operator-differential equations on the semi-axis

Abstract

In this work, we study a homogeneous fourth-order elliptic operator-differential equation with an unbounded operator under non-homogeneous boundary conditions on the semi-axis. We obtain sufficient conditions for the completeness of decreasing elementary solutions of the equation under study in the space of all its solutions from a fourth-order Sobolev type space.