2019
Том 71
№ 10

All Issues

Kasyanov P. O.

Articles: 4
Article (Ukrainian)

On the solvability of one class of parameterized operator inclusions

Kapustyan V. O., Kasyanov P. O., Kohut O. P.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2008. - 60, № 12. - pp. 1619–1630

We consider a class of parameterized operator inclusions with set-valued mappings of \( {\bar S_k} \) type. Sufficient conditions for the solvability of these inclusions are obtained and the dependence of the sets of their solutions on functional parameters is investigated. Examples that illustrate the results obtained are given.

Article (Ukrainian)

Evolution inequalities with noncoercive w λ 0 -pseudomonotone volterra-type mappings

Kasyanov P. O., Mel'nik V. S.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2008. - 60, № 11. - pp. 1499 – 1519

We consider a class of differential-operator inequalities with noncoercive w λ 0 -pseudomonotone operators. The problem of the existence of solutions of the Cauchy problem for these inequalities is investigated by using the Dubinsky method. A priori estimates for these solutions and their derivatives are obtained. We give a model example that illustrates the results and generalizations obtained.

Article (Ukrainian)

On properties of subdifferential mappings in Fréchet spaces

Kasyanov P. O., Mel'nik V. S.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2005. - 57, № 10. - pp. 1385–1394

We present conditions under which the subdifferential of a proper convex lower-semicontinuous functional in a Fréchet space is a bounded upper-semicontinuous mapping. The theorem on the boundedness of a subdifferential is also new for Banach spaces. We prove a generalized Weierstrass theorem in Fréchet spaces and study a variational inequality with a set-valued mapping.

Article (Ukrainian)

Global Attractor for a Nonautonomous Inclusion with Discontinuous Right-Hand Side

Kapustyan O. V., Kasyanov P. O.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2003. - 55, № 11. - pp. 1467-1475

We consider a nonautonomous inclusion the upper and lower selectors of whose right-hand side are determined by functions with discontinuities of the first kind. We prove that this problem generates a family of multivalued semiprocesses for which there exists a global attractor compact in the phase space.