It is now established that under quite general circumstances, including in models with jumps, the existence of a solution to a reflected BSDE is guaranteed under mild conditions, whereas the existence of a solution to a doubly reflected BSDE is essentially equivalent to the so-called Mokobodski condition. As for uniqueness of solutions, this holds under mild integrability conditions. However, f...

It is now established that under quite general circumstances, including in models with jumps, existence of a solution to a re ected BSDE is guaranteed under mild conditions, whereas existence of a solution to a doubly re ected BSDE is essentially equivalent to the so-called Mokobodski condition. As for uniqueness of solutions, it holds under mild integrability conditions. However, for practical...

We prove the existence and uniqueness of the mild solution for the 1D Vlasov-Poisson system with initial-boundary conditions by using iterated approximations. The same arguments yield existence and uniqueness for the free space or space periodic system. The major difficulty is the treatment of the boundary conditions. The main idea consists of splitting the velocities range by introducing criti...

Theorem 1.1. Consider (NLS) on Rd or Td, with μ = ±1. Fix s > d2 ; then (NLS) is locally well-posed in H s (in the sense of mild solutions): • Existence: For any u0 ∈ Hs, there exists a (mild) solution u defined on [0, T0], where T0 = cs‖u0‖ Hs, for a constant cs > 0. It is such that ‖u‖CT0Hs ≤ 2‖u0‖Hs. • Uniqueness: it is unique in LT0H s. • Dependence on the data: the map u0 7→ u is analytic ...

The objective of this paper is to study the existence and uniqueness of Mild solutions for a complex fuzzy evolution equation with nonlocal conditions that accommodates the notion of fuzzy sets defined by complex-valued membership functions. We first propose definition of complex fuzzy strongly continuous semigroups. We then give existence and uniqueness result relevant to the complex fuzzy evo...