Abstract version of the Cauchy-Kowalewski problem
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.
A fixed point theorem for affine mappings and its application to elasticity theory
In this paper we obtain a general fixed point theorem for an affine mapping in Banach space. As an application of this theorem we study existence of periodic solutions to the equations of the linear elasticity theory.
Bounded solutions to a system of second order ODEs and the Whitney pendulum
We give an existence theorem for bounded solutions to a system of second order ODEs. Dynamical applications are considered.
Evolution differential equations in Fréchet sequence spaces
We consider evolution differential equations in Fréchet spaces with unconditional Schauder basis, and construct a version of the majorant functions method to obtain existence theorems for Cauchy problems. Applications to PDE are also considered.
Peano type theorem for abstract parabolic equations
A note on existence theorem of Peano
An ODE with non-Lipschitz right hand side has been considered. A family of solutions with -dependence of the initial data has been obtained. A special set of initial data has been constructed. In this set the family is continuous. The measure of this set has been estimated.
Periodic solutions to Lagrangian system
A classical mechanics Lagrangian system with even Lagrangian is considered. The configuration space is a cylinder . A large class of nonhomotopic periodic solutions has been found.
On weak solutions to the Lagrange-d'Alembert equation
We consider nonholonomic systems with collisions and propose a concept of weak solutions to Lagrange-d'Alembert equations. Using this concept we describe the dynamics of collisions. Collisions of a rotating ball and a rough floor are considered.
A generalization of Schauder's theorem and its application to Cauchy-Kovalevskaya problem.
On regularity of stationary solutions to the Navier-Stokes equation in 3D torus.
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