相关论文: A perturbed time-dependent second-order sweeping p…

In this paper we study the existence of continuous solutions and their constructions for a second order iterative functional equation, which involves iterate of the unknown function and a nonlinear term. Imposing Lipschitz conditions to…

Integro-differential sweeping processes with prox-regular sets in Hilbert spaces have been the subject of various recent studies. Diverse applications of such differential inclusions to complementarity problems, electrical circuits,…

We present an optimization problem in infinite dimensions which satisfies the usual second-order sufficient condition but for which perturbed problems fail to possess solutions.

In this paper we provide a formulation for sweeping processes with arbitrary locally bounded retraction, not necessarily left or right continuous. Moreover we provide a proof of the existence and uniqueness of solutions for this formulation…

In this paper, we prove that there exists a unique, bounded continuous weak solution to the Dirichlet boundary value problem for a general class of second-order elliptic operators with singular coefficients, which does not necessarily have…

Conditions of the existence of solutions of linear and perturbed linear boundary value problems in the Hilbert spaces for the second order evolution equation are obtained.

In this paper, we study the existence of solutions to sweeping processes in the presence of stochastic perturbations, where the moving set takes uniformly prox-regular values and varies continuously with respect to the Hausdorff distance,…

For a class of fully nonlinear equations having second order operators which may be singular or degenerate when the gradient of the solutions vanishes, and having first order terms with power growth, we prove the existence and uniqueness of…

A singularly perturbed linear system of second order partial differential equations of parabolic reaction-diffusion type with given initial and boundary conditions is considered. The leading term of each equation is multiplied by a small…

In this paper we present time-dependent perturbations of second-order non-autonomous abstract Cauchy problems associated to a family of operators with constant domain. We make use of the equivalence to a first-order non-autonomous abstract…

This paper describes a new numerical method for solving eigenstate problems, such as time-independent Schrodinger equation. The idea is to use the first order perturbation theory to rewrite the eigenvalue problem as a system of first order…

In the setting adopted by Edmond and Thibault [Mathematical Programming 104 (2005), 347--373], we study a class of perturbed sweeping processes. Under suitable assumptions, we obtain two solution existence theorems for perturbed sweeping…

We study an abstract second order inclusion involving two nonlinear single-valued operators and a nonlinear multivalued term. Our goal is to establish the existence of solutions to the problem by applying numerical scheme based on time…

This article concerns second-order time discretization of subdiffusion equations with time-dependent diffusion coefficients. High-order differentiability and regularity estimates are established for subdiffusion equations with…

We consider a singularly perturbed reaction diffusion problem as a first order two-by-two system. Using piecewise discontinuous polynomials for the first component and $H_{div}$-conforming elements for the second component we provide a…

The aim of this paper is twofold. On one hand we prove that the Moreau's sweeping process driven by a uniformly prox-regular moving set with local bounded retraction has a unique solution provided that the coefficient of prox-regularity is…

In this note, we show a classical result on the local existence and uniqueness of a solution to an initial value problem subject to a Lipschitz condition. We use only elementary tools from mathematical analysis, without involving any…

We consider a singularly perturbed fourth-order problem with third-order terms on the unit square. With a formal power series approach, we decompose the solution into solutions of reduced (third-order) problems and various layer parts. The…

We give an algorithm for the class of second order unification problems in which second order variables have at most one occurrence.

Here we present well-posedness results for first order stochastic differential inclusions, more precisely for sweeping process with a stochastic perturbation. These results are provided in combining both deterministic sweeping process…