On a problem for operator-differential second-order equations with nonlocal boundary condition

An operator-differential second-order equation with nonlocal boundary condition at zero is considered on the semiaxis. Here we give sufficient conditions on the operator coefficients for the regular solvability of the boundary-value problem. Moreover, we obtain conditions for the completeness andminimality of the derivative of the chain of eigen- and associated vectors generated by the boundary-value problem under study and establish the completeness and minimality of the decreasing elementary solutions of the operator-differential equation under consideration.