In this paper, we deal with the Lp(p1) solutions to one dimensional backward stochastic differential equations (BSDEs) with discontinuous generators. We obtain an existence theorem of Lp solutions for BSDEs whose generators satisfy a kind of discontinuous condition in y and are uniformly...

In this paper, we introduce the symmetric strong vector quasi-equilibrium problem. We then demonstrate that the symmetric strong vector quasi-equilibrium problem is solvable under the suitable assumptions. As an application, we get an existence theorem of the strong saddle points of...

This paper is devoted to the Levitin–Polyak well-posedness by perturbations for a class of general systems of set-valued vector quasi-equilibrium problems (SSVQEP) in Hausdorff topological vector spaces. Existence of solution for the system of set-valued vector quasi-equilibrium problem with...

In this paper, we study the structure of trajectories of discrete disperse dynamical systems with a Lyapunov function which are generated by set-valued mappings. We establish a weak version of the turnpike property which holds for all trajectories of such dynamical systems which are of a...

We first present a proper condition under which the image of a set-valued mapping becomes a singleton and then obtain several generic uniqueness theorems which can be applied to study the uniqueness of the solutions for nonlinear problems. As applications, we prove that, in the sense of Baire...

In this paper, by virtue of the separation theorem of convex sets, we prove a minimax theorem, a cone saddle point theorem and a Ky Fan minimax theorem for a scalar set-valued mapping under nonconvex assumptions of its domains, respectively. As applications, we obtain an existence result for the...

Set-valued optimisation is an important topic and has wide applications in engineering and game theory. An interesting topic in set-valued optimisation is the appropriate introduction of a derivative concept for set-valued mappings. In this paper, Dini directional derivatives are introduced and...

Set-valued optimisation is an important topic and has wide applications in engineering and game theory. An interesting topic in set-valued optimisation is the appropriate introduction of a derivative concept for set-valued mappings. In this paper, Dini directional derivatives are introduced and...

In this paper, we introduce a more general form of vector equilibrium problems with a moving ordering cone and set-valued mappings, and obtain some existence theorems for generalized vector equilibrium problems, which extend and unify some existence results for similar problems. Copyright...