In this paper, we study the uniqueness of solutions for diagonal hyperbolic systems in one space dimension. We present two uniqueness results. The first one is a global existence and uniqueness result of a continuous solution for strictly hyperbolic systems. The second one is a global existence and uniqueness result of a Lipschitz solution for hyperbolic systems not necessarily strictly hyperbo...

In this paper, we study the uniqueness of solutions for diagonal hyperbolic systems in one space dimension. We present two uniqueness results. The first one is a global existence and uniqueness result of a continuous solution for strictly hyperbolic systems. The second one is a global existence and uniqueness result of a Lipschitz solution for hyperbolic systems not necessarily strictly hyperbo...

in this article, we investigate sufficient conditions for existence of maximal and minimalsolutions to a coupled system of highly nonlinear differential equations of fractional order with mixedtype boundary conditions. to achieve this goal, we apply monotone iterative technique togetherwith the method of upper and lower solutions. also an error estimation is given to check theaccuracy of the me...

In this paper we extend recent results on the existence and uniqueness of solutions of ODEs with non-smooth vector fields to the case of martingale solutions, in the StroockVaradhan sense, of SDEs with non-smooth coefficients. In the first part we develop a general theory, which roughly speaking allows to deduce existence, uniqueness and stability of martingale solutions for L-almost every init...