On difference schemes for quasilinear evolution problems.
On differential equations and inclusions with mean derivatives on a compact manifold
We introduce and investigate a new sort of stochastic differential inclusions on manifolds, given in terms of mean derivatives of a stochastic process, introduced by Nelson for the needs of the so called stochastic mechanics. This class of stochastic inclusions is ideologically the closest one to ordinary differential inclusions. For inclusions with forward mean derivatives on manifolds we prove some results on the existence of solutions.
On differential inclusions of velocity hodograph type with Carathéodory conditions on Riemannian manifolds
We investigate velocity hodograph inclusions for the case of right-hand sides satisfying upper Carathéodory conditions. As an application we obtain an existence theorem for a boundary value problem for second-order differential inclusions on complete Riemannian manifolds with Carathéodory right-hand sides.
On differential inclusions with prescribed solutions
On Differential Inclusions with Unbounded Right-Hand Side
2000 Mathematics Subject Classification: 58C06, 47H10, 34A60.The classical Filippov’s Theorem on existence of a local trajectory of the differential inclusion [x](t) О F(t,x(t)) requires the right-hand side F(·,·) to be Lipschitzian with respect to the Hausdorff distance and then to be bounded-valued. We give an extension of the quoted result under a weaker assumption, used by Ioffe in [J. Convex Anal. 13 (2006), 353-362], allowing unbounded right-hand side.
On discontinuous implicit differential equations in ordered Banach spaces with discontinuous implicit boundary conditions
We consider the existence of extremal solutions to second order discontinuous implicit ordinary differential equations with discontinuous implicit boundary conditions in ordered Banach spaces. We also study the dependence of these solutions on the data, and cases when the extremal solutions are obtained as limits of successive approximations. Examples are given to demonstrate the applicability of the method developed in this paper.
On discrete analogues of nonlinear implicit differential equations.
On distributional solutions of some systems of linear differential equations
On efficient method for system of fractional differential equations.
On equation of finite type, 1-special, with the same central dispersion of the first kind
On Euler methods for Caputo fractional differential equations
Numerical methods for fractional differential equations have specific properties with respect to the ones for ordinary differential equations. The paper discusses Euler methods for Caputo differential equation initial value problem. The common properties of the methods are stated and demonstrated by several numerical experiments. Python codes are available to researchers for numerical simulations.
On eventual stability of impulsive systems of differential equations.
On evolution inclusions associated with time dependent convex subdifferentials
On exact controllability of first-order impulsive differential equations.
On Existence and Asymptotic Properties of Kneser Solutions to Singular Second Order ODE.
We investigate an asymptotic behaviour of damped non-oscillatory solutions of the initial value problem with a time singularity , , on the unbounded domain . Function is locally Lipschitz continuous on and has at least three zeros , and . The initial value . Function is continuous on has a positive continuous derivative on and . Asymptotic formulas for damped non-oscillatory solutions and their first derivatives are derived under some additional assumptions. Further, we provide...
On existence of Kneser solutions of a certain class of -th order nonlinear differential equations
The paper deals with existence of Kneser solutions of -th order nonlinear differential equations with quasi-derivatives.
On existence of oscillatory solution of the system of differential equations
On extremal solutions to infinite dimensional non-linear second order systems
On first integrals for polynomial differential equations on the line
We show that any equation dy/dx = P(x,y) with P a polynomial has a global (on ℝ²) smooth first integral nonconstant on any open domain. We also present an example of an equation without an analytic primitive first integral.
On formal theory of differential equations. II.