2018
Том 70
№ 11

All Issues

Statkevych V. M.

Articles: 3
Article (Ukrainian)

Investigation of solutions of boundary-value problems with essentially infinite-dimensional elliptic operator

Statkevych V. M.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2012. - 64, № 2. - pp. 229-236

We consider Dirichlet problems for the Poisson equation and linear and nonlinear equations with essentially infinite-dimensional elliptic operator (of the Laplace -Levy type). The continuous dependence of solutions on boundary values and sufficient conditions for increasing the smoothness of solutions are investigated.

Article (Ukrainian)

Systems of essentially infinite-dimensional differential equations

Statkevych V. M.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2011. - 63, № 9. - pp. 1257-1262

We investigate systems of differential equations with essentially infinite-dimensional elliptic operators (of the Laplace - Levy type). For nonlinear systems, we prove theorems on the existence and uniqueness of solutions. For a linear system, we give an explicit formula for the solution.

Brief Communications (Ukrainian)

Nonlinear equations with essentially infinite-dimensional differential operators

Bogdanskii Yu. V., Statkevych V. M.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2010. - 62, № 11. - pp. 1571–1576

We consider nonlinear differential equations and boundary-value problems with essentially infinite-dimensional operators (of the Laplace–Lévy type). An analog of the Picard theorem is proved.