This paper deals with the existence and uniqueness of mild solutions to neutral stochastic delay functional integro-differential equations perturbed by a fractional Brownian motion
We define an integral approximation for the modulus of the gradient |?
We introduce a space
Let
This paper is interested in solving a multidimensional backward stochastic differential equation (BSDE) whose generator satisfies the Osgood condition in
This article presents a complete discretization of a nonlinear Sobolev equation using space-time discontinuous Galerkin method that is discontinuous in time and continuous in space. The scheme is formulated by introducing the equivalent integral equation of the primal equation. The proposed scheme does not explicitly include the jump terms in time, which represent the discontinuity characteristics of approximate solution. And then the complexity of the theoretical analysis is reduced. The existence and uniqueness of the approximate solution and the stability of the scheme are proved. The optimalorder error estimates in
Suppose that
Variable-weight optical orthogonal code (OOC) was introduced by G. C. Yang [IEEE Trans. Commun., 1996, 44: 47-55] for multimedia optical CDMA systems with multiple quality of service (QoS) requirements. In this paper, seven new infinite classes of optimal (
We give the growth properties of harmonic functions at infinity in a cone, which generalize the results obtained by Siegel-Talvila.
The Herz type Besov and Triebel-Lizorkin spaces with variable exponent are introduced. Then characterizations of these new spaces by maximal functions are given.
Let
We introduce the generalized Jacobi-Gauss-Lobatto interpolation involving the values of functions and their derivatives at the endpoints, which play important roles in the Jacobi pseudospectral methods for high order problems. We establish some results on these interpolations in non-uniformly weighted Sobolev spaces, which serve as the basic tools in analysis of numerical quadratures and various numerical methods of differential and integral equations.
Let
We determine the derivation algebra and the automorphism group of the generalized topological
Let {