Necessary and sufficient conditions for global-in-time existence of solutions of ordinary, stochastic, and parabolic differential equations.
On the two-point boundary value problem for quadratic second-order differential equations and inclusions on manifolds.
Conditions for global existence of solutions of ordinary differential, stochastic differential, and parabolic equations.
On a two-point boundary value problem for second-order differential inclusions on Riemannian manifolds.
Stochastic differential inclusions of Langevin type on Riemannian manifolds
We introduce and investigate a set-valued analogue of classical Langevin equation on a Riemannian manifold that may arise as a description of some physical processes (e.g., the motion of the physical Brownian particle) on non-linear configuration space under discontinuous forces or forces with control. Several existence theorems are proved.
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.
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