This article presents the results on existence, uniqueness and stability of mild solutions of impulsive stochastic semilinear neutral functional differential equations without a Lipschitz condition and with a Lipschitz condition. The results are obtained by using the method of successive approximations. 2000 Mathematical Subject Classification: 93E15,60H15,35R12.

This article presents the results on existence, uniqueness and stability of mild solution for impulsive stochastic semilinear functional differential equations with non-Lipschitz condition and Lipschitz condition. The results are obtained by using the method of successive approximation and Bihari’s inequality.

In this paper we describe the notion of a weak lipschitzianity of a mapping on a C stratification. We also distinguish a class of regularity conditions that are in some sense invariant under definable, locally Lipschitz and weakly bi-Lipschitz homeomorphisms. This class includes the Whitney (B) condition and the Verdier condition.

In this paper, we study the existence of asymptotic almost automorphic solution of fractional neutral integro-differential equation. We prove the result by using fixed point theorems. We show the result with Lipschitz condition and without Lipschitz condition on the forcing term. Finally examples are given to illustrate the analytical findings. Mathematics Subject Classification(2010): 34A08, 1...

We denote by (P ) the problem given by the equation (1), the boundary condition (2) and the initial condition (3). We assume that the function c satisfies the hypothesis (Hc) c is a continuous nondecreasing function such that c ′ ∈ Lloc(R); and that the initial condition u0 and the boundary data u D satisfy the hypotheses (H0) u0 ∈ L∞(Ω) and we define U0 := ‖u0‖L∞(Ω); (HD) u D is Lipschitz cont...

using a generalized spherical mean operator, we obtain a generalization of titchmarsh&apos;s theorem for the dunkl transform for functions satisfying the (&apos;; p)-dunkl lipschitz condition in the space lp(rd;wl(x)dx), 1 < p 6 2, where wl is a weight function invariant under the action of an associated re ection group.

in this paper‎, ‎using a generalized dunkl translation operator‎, ‎we obtain a generalization of titchmarsh&apos;s theorem for the dunkl transform for functions satisfying the$(psi,p)$-lipschitz dunkl condition in the space $mathrm{l}_{p,alpha}=mathrm{l}^{p}(mathbb{r},|x|^{2alpha+1}dx)$‎, ‎where $alpha>-frac{1}{2}$.

We present and analyse two implicit methods for Ito stochastic differential equations (SDEs) with Poisson-driven jumps. The first method, SSBE, is a split-step extension of the backward Euler method. The second method, CSSBE, arises from the introduction of a compensated, martingale, form of the Poisson process. We show that both methods are amenable to rigorous analysis when a one-sided Lipsch...