Nomirovs'kii D. A.
Ukr. Mat. Zh. - 2010. - 62, № 8. - pp. 1011–1021
We propose an approach to the investigation of generalized solutions of linear operators that satisfy weakened a priori inequalities. This approach generalizes several well-known definitions of generalized solutions of operator equations. We prove existence and uniqueness theorems for a generalized solution.
Ukr. Mat. Zh. - 2006. - 58, № 6. - pp. 778–786
We consider analogs of the Galerkin method for a linear wave equation of the fifth order with generalized functions on the right-hand side. Theorems on the convergence of an approximate method, depending on the order of singularity of the right-hand side, are proved.
Ukr. Mat. Zh. - 2005. - 57, № 3. - pp. 366–376
We consider the problem of solvability and optimization for a pseudohyperbolic operator of the general form. We prove theorems on existence and uniqueness for various right-hand sides of the equation. The results obtained are applied to the problem of trajectory-final controllability.
Ukr. Mat. Zh. - 2004. - 56, № 12. - pp. 1707-1716
For a sufficiently broad class of partial differential operators, we prove a theorem on homeomorphisms. Applications of this theorem to some classical operators are considered.