Speciality:
01.01.01 (Real analysis, complex analysis, and functional analysis)
E-mail: Website: https://mipt.ru/education/chair/mathematics/tutors/professors/dymarsky.php Keywords: spectral theory of linear self-adjoint operators; spectral theory of nonlinear operators; global (nonlinear) analysis.
UDC: 512.643, 517.927, 517.956, 517.983, 517.984, 517.984.46, 517.988, 517.988.57, 517.927.25, 517.988.2 MSC: 34b24, 35j10, 35p30, 47a75, 47h12, 58e07, 58f19
Subject:
For periodic eigenvalue problem family (where a potential serves as a parameter) a topological properties of manifolds of eigenfunctions with fixed number of zeros are investigated. Quasilinear eigenvector problems $A(u)u = \lambda u$ ($A$ is a map into the space of compact self-adjoint operators) are considered and their homotopic classification is presented. New eigenvectors theorems are obtained.
Main publications:
Dymarskii Ya. M. On manifolds of self-adjoint elliptic operators with multiple eigenvalues // Methods of Functional Analysis and Topology, 2001, 7(2), 68–74.
Dymarskii Ya. M. The Periodic Choquard Equation // Operator Theory: Advances and Applications, 2000, 117, 87–99.
