Mirzoev S. S.
On holomorphic solutions of some boundary-value problems for second-order elliptic operator differential equations
Ukr. Mat. Zh. - 2011. - 63, № 3. - pp. 416-420
In the class of holomorphic vector functions, we determine conditions of the solvability of boundary-value problem for a class of second-order differential operator equations, which are given in terms of operator coefficients containing in the equation and in the boundary condition.
On solutions of one class of second-order operator differential equations in the class of holomorphic vector functions
Ukr. Mat. Zh. - 2010. - 62, № 6. - pp. 801–813
We establish sufficient conditions for the completeness of a part of root vectors of one class of the second-order operator bundles corresponding to the characteristic numbers from a certain sector and prove the theorem on completeness of a system of elementary holomorphic solutions of the corresponding second-order homogeneous operator differential equations. We also indicate the conditions of correct and unique solvability of a boundary-value problem for the analyzed equation with linear operator in the boundary condition and estimate the norm of the operator of the intermediate derivative in the perturbed part of the equation.