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.

We prove the Lipschitz dependence on the initial condition of the solution set of a nonconvex second-order differential inclusions by applying the contraction principle in the space of selections of the multifunction instead of the space of solutions.

Objective: The purpose of the present study was investigation of eight weeks high intensity interval (HIIT) along with curcumin supplementation on liver Glutathione Peroxidase (GPX) Activity & Malondialdehyde (MDA) Concentration among diabetic male rats. Materials and Methods: Thirty-two male mice were divided to four groups of control-diabetic, exercise-diabetic, supplementary-diabetic, and e...

We obtain a complete description of closed ideals of the algebra D ∩ lip α , 0 < α ≤ 1 2 , where D is the Dirichlet space and lip α is the algebra of analytic functions satisfying the Lipschitz condition of order α.