Existence and uniqueness result for multidimensional BSDEs with generators of Osgood type

This paper is interested in solving a multidimensional backward stochastic differential equation （BSDE） whose generator satisfies the Osgood condition in y and the Lipschitz condition in z. We establish an existence and uniqueness result of solutions for this kind of BSDEs, which generalizes some known results.

L^p Solutions of BSDEs with a New Kind of Non-Lipschitz Coefficients

In this paper, we are interested in solving multidimensional backward stochastic differential equations(BSDEs) with a new kind of non-Lipschitz coefficients. We establish an existence and uniqueness result of the L^p(p > 1) solutions, which includes some known results as its particular cases.

L^p(p > 1) Solutions of BSDEs with Generators Satisfying Some Non-uniform Conditions in t and ω

This paper is devoted to the L^p(p > 1) solutions of one-dimensional backward stochastic differential equations(BSDEs for short) with general time intervals and generators satisfying some non-uniform conditions in t and ω. An existence and uniqueness result,a comparison theorem and an existence result for the minimal solutions are respectively obtained, which considerably improve some known works. Some classical techniques used to deal with the existence and uniqueness of L^p(p > 1) solutions of BSDEs with Lipschitz or linear-growth generators are also developed in this paper.

The instability of an elastic planet with a liquid core

Considering a spherical planet with a liquid core surrounded by a solid shell,we developed a quasi-static model to investigate the deformation of the double-layered planet with self-gravity and obtained the boundary value problem about radial equilibrium,which is solved by the numerical methods.The effects of governing parameters about geometry,density and bulk modulus on the deformation of the planet with self-gravity were discussed.In addition,we also developed the incremental equation theory to investigate the stability of the double-layered planet under its own gravity.It is concluded that instability is more likely to occur on the planet with smaller liquid cores when the outer radius and density of the planets are constant.Although we only study special double-layered planets,these methods can be conveniently extended to complex multi-layered planets.

General time interval multidimensional BSDEs with generators satisfying a weak stochastic-monotonicity condition

This paper establishes an existence and uniqueness result for the adapted solution of a general time interval multidimensional backward stochastic differential equation (BSDE), where the generator g satisfies a weak stochastic-monotonicity condition and a general growth condition in the state variable y, and a stochastic-Lipschitz condition in the state variable z. This unifies and strengthens some known works. In order to prove this result, we develop some ideas and techniques employed in Xiao and Fan [25] and Liu et al. [15]. In particular, we put forward and prove a stochastic Gronwall-type inequality and a stochastic Bihari-type inequality, which generalize the classical ones and may be useful in other applications. The martingale representation theorem, Itô’s formula, and the BMO martingale tool are used to prove these two inequalities.

BSDEs with stochastic Lipschitz condition:A general result

We prove a general existence and uniqueness result of solutions for a backward stochastic differential equation(BSDE)with a stochastic Lipschitz condition.We also establish a continuous dependence property and a comparison theorem for solutions to this type of BSDEs,thus strengthening existing results.