Lipschitz condition

In this paper, we introduce a tamed-adaptive Euler-Maruyama approximation scheme for stochastic differential equations with Markovian switching. We show that the scheme converges in L 1 -norm when applying for SDEs with locally Lipschitz continuous drift and locally Holder continuous diffusion.

21p visharma 20-10-2023 6 2   Download

The paper is organized as follows. In the next section, Section 2, we recall some notions and basic properties of analysis on time scales. Section 3 presents the form of Hardy’s inequalities on time scales and its proof.

10p viberkshire 09-08-2023 7 5   Download

In this paper, we introduce a new approximate projection algorithm for finding a common solution of multivalued variational inequality problems and fixed point problems in a real Hilbert space. The proposed algorithm combines the approximate projection method with the Halpern iteration technique. The strongly convergent theorem is established under mild conditions.

7p viharry 15-12-2022 15 2   Download

In this paper, we consider an explicit method that is strong convergence in an infinite-dimensional Hilbert space and a simple variant of the hybrid steepest-descent method, introduced by Yamada. The strong convergence of this method is proved under some mild conditions. Finally, we give an application for the optimization problem and present some numerical experiments to illustrate the effectiveness of the proposed algorithm.

8p spiritedaway36 28-11-2021 8 1   Download

Consider a stochastic evolution equation containing Stratonovich-multiplicative white noise of the form ( , ) du Au f t u u W dt     where the partial differential operator A is positive definite, self-adjoint with a discrete spectrum; and the nonlinear part f satisfies the Lipschitz condition with  belonging to an admissible function space. We prove the existence of a (stochastic) inertial manifold for the solutions to the above equation. Our method relies on the Lyapunov-Perron equation in a combination with the admissibility of function spaces.

16p trinhthamhodang1218 18-03-2021 9 2   Download

The concept of approximation introduced by D.T. Luc et al. [1] as a generalized derivative for non-Lipschitz vector functions to consider vector problems with non-Lipschitz data under inclusion constraints. Some calculus of approximations are presented. A necessary optimality condition, a type of KKT condition, for local efficient solutions of the problems is established under an assumption on regularity. Applications and numerical examples are also given.

11p nguaconbaynhay9 03-12-2020 14 1   Download

A class of multiobjective fractional programming problems (MFP) is considered where the involved functions are locally Lipschitz. In order to deduce our main results, we introduce the definition of (p,r) − ρ − (η,θ) - invex class about the Clarke generalized gradient. Under the above invexity assumption, sufficient conditions for optimality are given. Finally, three types of dual problems corresponding to (MFP) are formulated, and appropriate dual theorems are proved.

20p vinguyentuongdanh 19-12-2018 26 1   Download

In this paper, we define some new generalizations of strongly convex functions of order m for locally Lipschitz functions using Clarke subdifferential. Suitable examples illustrating the non emptiness of the newly defined classes of functions and their relationships with classical notions of pseudoconvexity and quasiconvexity are provided.

16p danhnguyentuongvi27 19-12-2018 37 1   Download

We present some duality theorems for a non-smooth Lipschitz vector optimization problem. Under generalized invexity assumptions on the functions the duality theorems do not require constraint qualifications.

7p vinguyentuongdanh 19-12-2018 32 0   Download

In this paper we study Lipschitz solutions of partial differential relations of the form (1) ∇u(x) ∈ K a.e. in Ω, where u is a (Lipschitz) mapping of an open set Ω ⊂ Rn into Rm , ∇u(x) is its gradient (i.e. the matrix ∂ui (x)/∂xj , 1 ≤ i ≤ m, 1 ≤ j ≤ n, defined for almost every x ∈ Ω), and K is a subset of the set M m×n of all real m × n matrices. In addition to relation (1), boundary conditions and other conditions on u will also be considered. Relation (1)...

29p tuanloccuoi 04-01-2013 51 8   Download

MULTIPLE SOLUTIONS FOR QUASILINEAR ELLIPTIC NEUMANN PROBLEMS IN ORLICZ-SOBOLEV SPACES NIKOLAOS HALIDIAS AND VY K. LE Received 15 October 2004 and in revised form 21 January 2005 We investigate the existence of multiple solutions to quasilinear elliptic problems containing Laplace like operators (φ-Laplacians). We are interested in Neumann boundary value problems and our main tool is Br´ zis-Nirenberg’s local linking theorem. e 1. Introduction In this paper, we consider the following elliptic problem with Neumann boundary condition, −div α ∇u(x) ∇u(x) = g(x,u) a.e. on Ω (1.1) ∂u = 0 a.e.

8p sting12 10-03-2012 25 2   Download

PERIODIC BOUNDARY VALUE PROBLEMS ON TIME SCALES ´ PETR STEHLIK Received 20 April 2004 We extend the results concerning periodic boundary value problems from the continuous calculus to time scales. First we use the Schauder fixed point theorem and the concept of lower and upper solutions to prove the existence of the solutions and then we investigate a monotone iterative method which could generate some of them. Since this method does not work on each time scale, a condition containing a Lipschitz constant of right-hand side function and the supremum of the graininess function is introduced.

12p sting12 10-03-2012 47 6   Download