In this paper we apply the gravitational decoupling method for dynamical systems in order to obtain a new type of solution which can describe hairy black hole. We consider three cases decoupling. The first one is simplest and well-known when mass function only space coordinate $r$. second case Vaidya spacetime depends on time $v$ . And third represents generalization these two cases: both $r$ $...

In this paper, by virtue of the properties generalized inverses elements in rings with involution, we construct related equations. By discussing solutions these equations, invertible are characterized.

Within the nonlinear theory of generalized functions introduced earlier by the author a number of existence and regularity results have been obtained. One of them has been the first global version of the Cauchy-Kovalevskaia theorem, which proves the existence of generalized solutions on the whole of the domain of analyticity of arbitrary analytic nonlinear PDEs. These generalized solutions are ...

In this paper, we study existence and approximation of solutions to some threepoint boundary value problems for fractional differential equations of the type Dq 0+u(t) + f(t, u(t)) = 0, t ∈ (0, 1), 1 < q < 2 u′(0) = 0, u(1) = ξu(η), where 0 < ξ, η ∈ (0, 1) and Dq 0+ is the fractional derivative in the sense of Caputo. For the existence of solution, we develop the method of upper and lower solut...

Using a collective field method, we obtain explicit solutions of the generalized CalogeroSutherland models that are characterized by the roots of the classical groups BN and CN . Starting from the explicit wave functions for AN−1 type expressed in terms of the singular vectors of the WN algebra, we give a systematic method to construct wave functions and derive energy eigenvalues for other type...

Robust asymptotic stability for hybrid systems is considered. For this purpose, a generalized solution concept is developed. The first step is to characterize a hybrid time domain that permits an efficient description of the convergence of a sequence of solutions. Graph convergence is used. Then a generalized solution definition is given that leads to continuity with respect to initial conditio...