arXiv subjects
Publications and source records attributed to Oleg Zubelevich.
We consider a semilinear elliptic equation in a bounded domain with zero boundary conditions. The nonlinearity is discontinuous and monotone, but it is not a Carathéodory's function. The existence theorem has been proved.
We generalise the Caristi Fixed Point Theorem to the mappings of the complete semi-metric spaces.
The Lagrange-d'Alembert equations with constraints belonging to $H^{1,\infty}$ have been considered. A concept of weak solutions to these equations has been built. Global existence theorem for Cauchy problem has been obtained.
We consider evolution differential equations in Fréchet spaces that possess unconditional Schauder basis and construct a version of the majorant functions method to obtain existence theorems for Cauchy problems. Applications to PDE and ODE have been considered.
We propose the existence theorem for bounded solutions to the system of 2-nd order ODE. Dynamical applications have been considered.
We consider nonholonomic systems with collisions and propose a concept of weak solutions to Lagrange-d'Alembert equations. In the light of this concept we describe dynamics of the collisions. Several applications have been investigated. Particularly the collision of rotating ball and the rough floor has been considered.
We consider parabolic problems with non-Lipschitz nonlinearity in the different scales of Banach spaces and prove local-in-time existence theorem. New class of parabolic equations that have analytic solutions is obtained.
We consider an abstract version of the Cauchy-Kowalewski Problem with the right hand side being free from the Lipschitz type conditions and prove the existence theorem.
We consider NSE with $H^1$-initial conditions on the 3-dimensional torus and prove that there exists a solution that is analytic in all variables.