Multi-dimensional uncertain differential equation is a system of uncertain differential equations driven by amulti-dimensional Liu process. This paper first gives the analytic solutions of two special types of multi-dimensional uncertain differential equations. After that, it proves that the multi-dimensional uncertain differential equation has a unique solution provided that its coefficients s...

We characterise the weak $$^*$$ symmetric strong diameter 2 property in Lipschitz function spaces by a of its predual, Lipschitz-free space. call this new decomposable octahedrality and study duality with general. For Banach space to be decomposably octahedral it is sufficient that dual has property. Whether also necessary condition remains open.

In this paper, we study the reflected BSDE with one continuous barrier, under the monotonicity and general increasing condition on y and non Lipschitz condition on z. We prove the existence and uniqueness of the solution to these equation by approximation method.

Keywords: Stochastic differential delay equation (SDDE) Split-step theta scheme Stochastic linear theta scheme Strong convergence rate Exponential mean square stability a b s t r a c t This paper establishes the boundedness, convergence and stability of the two classes of theta schemes, namely split-step theta (SST) scheme and stochastic linear theta (SLT) scheme, for stochastic differential de...

Using a Lipschitz type condition, we obtain the uniqueness of solutions for a system of n-th order nonlinear ordinary differential equations where the coefficients are allowed to have singularities.

In this paper, we investigate the existence and uniqueness of fuzzy solutions for semilinear fuzzy integrodifferential equations using integral contractor. The notion of ’bounded integral contractor’, introduced by Altman [1], is weaker than Lipschitz condition.

A generalization of the Flow-box Theorem is proven. The assumption of a C vector field f is relaxed to the condition that f be locally Lipschitz. The theorem holds in any Banach space.

We give a necessary and sufficient condition for a difference of convex (DC, for short) functions, defined on a normed space, to be Lipschitz continuous. Our criterion relies on the intersection of the ε-subdifferentials of the involved functions.

Let g be a locally Lipschitz continuous real valued function which satisfies the KellerOsserman condition and is convex at infinity, then any large solution of −∆u+ g(u) = 0 in a ball is radially symmetric. 1991 Mathematics Subject Classification. 35J60 .

Some results on convergence of Newton’s method in Banach spaces are established under the assumption that the derivative of the operators satisfies the radius or center Lipschitz condition with a weak L average.