In this paper,we first prove the existence of the global attractor Aν ∈ C（[-ν,0],2）（ν 0） for a weak damping discrete nonlinear Schrdinger equation with delay.Then we consider an upper semi-continuity of Aν as...In this paper,we first prove the existence of the global attractor Aν ∈ C（[-ν,0],2）（ν 0） for a weak damping discrete nonlinear Schrdinger equation with delay.Then we consider an upper semi-continuity of Aν as ν → 0＋.展开更多
This paper is concerned with the pullback dynamics and robustness for the 2D incompressible Navier-Stokes equations with delay on the convective term in bounded domain.Under appropriate assumption on the delay term,we...This paper is concerned with the pullback dynamics and robustness for the 2D incompressible Navier-Stokes equations with delay on the convective term in bounded domain.Under appropriate assumption on the delay term,we establish the existence of pullback attractors for the fluid flow model,which is dependent on the past state.Inspired by the idea in Zelati and Gal’s paper(JMFM,2015),the robustness of pullback attractors has been proved via upper semi-continuity in last section.展开更多
Let S = {1,1/2,1/2^2,…,1/∞ = 0} and I = [0, 1] be the unit interval. We use ↓USC（S） and ↓C（S） to denote the families of the regions below of all upper semi-continuous maps and of the regions below of all conti...Let S = {1,1/2,1/2^2,…,1/∞ = 0} and I = [0, 1] be the unit interval. We use ↓USC（S） and ↓C（S） to denote the families of the regions below of all upper semi-continuous maps and of the regions below of all continuous maps from S to I and ↓C0（S） = {↓f∈↓C（S） ： f（0） = 0}. ↓USC（S） endowed with the Vietoris topology is a topological space. A pair of topological spaces （X, Y） means that X is a topological space and Y is its subspace. Two pairs of topological spaces （X, Y） and （A, B） are called pair-homeomorphic （≈） if there exists a homeomorphism h ： X→A from X onto A such that h（Y） = B. It is proved that, （↓USC（S）,↓C0（S）） ≈（Q, s） and （↓USC（S）,↓C（S）／ ↓C0（S））≈（Q, c0）, where Q = [-1,1]^ω is the Hilbert cube and s = （-1,1）^ω,c0= {（xn）∈Q ： limn→∞= 0}. But we do not know what （↓USC（S）,↓C（S））is.展开更多
Let X, Y be two finite-dimensional topological vector spaces, Z a Hausdorff topological vector space, K C X and D C Z be two nonempty sets, C be a pointed, closed, and convex cone in Y with int C ≠θ Let S ： K → 2^...Let X, Y be two finite-dimensional topological vector spaces, Z a Hausdorff topological vector space, K C X and D C Z be two nonempty sets, C be a pointed, closed, and convex cone in Y with int C ≠θ Let S ： K → 2^K and T ： K → 2^D be two multivalued mappings, and φ ： K × D × K → Y be a trifunction. In this paper, we consider the generalized vector quasi-equilibrium problem, which is formulated by finding X∈ K and y∈ T（x） such that x∈ E S（x） and φ（x,y, u） （∈/） -int C for all u ∈ S（x）. We establish an existence result in which T is not supposed to have any continuity property. Our results extend and improve the corresponding results of Cubiotti, Yao and Guo.展开更多
This paper is concerned with the existence and upper semi-continuity of random attractors for the nonclassical diffusion equation with arbitrary polynomial growth nonlinearity and multiplicative noise in H<sup>1...This paper is concerned with the existence and upper semi-continuity of random attractors for the nonclassical diffusion equation with arbitrary polynomial growth nonlinearity and multiplicative noise in H<sup>1</sup>(R<sup>n</sup>). First, we study the existence and uniqueness of solutions by a noise arising in a continuous random dynamical system and the asymptotic compactness is established by using uniform tail estimate technique, and then the existence of random attractors for the nonclassical diffusion equation with arbitrary polynomial growth nonlinearity. As a motivation of our results, we prove an existence and upper semi-continuity of random attractors with respect to the nonlinearity that enters the system together with the noise.展开更多
基金Supported by the National Natural Science Foundation of China (No.10771139,10826091)the Natural Science Foundation of Wenzhou University with item (No.2007L024)+3 种基金the Innovation Program of Shanghai Municipal Education Commission (No.08ZZ70)Leading Academic Discipline Project of Shanghai Normal University(No.DZL707)Foundation of Shanghai Normal University (No.DYL200803,PL715)Natural Science Foundation of Zhejiang Province (No.Y6080077)
文摘In this paper,we first prove the existence of the global attractor Aν ∈ C（[-ν,0],2）（ν 0） for a weak damping discrete nonlinear Schrdinger equation with delay.Then we consider an upper semi-continuity of Aν as ν → 0＋.
基金Xin-Guang Yang was partially supported by the Fund of Young Backbone Teacher in Henan Province(No.2018GGJS039)cultivation Fund of Henan Normal University(No.2020PL17)Henan Overseas Expertise Introduction Center for Discipline Innovation(No.CXJD2020003).
文摘This paper is concerned with the pullback dynamics and robustness for the 2D incompressible Navier-Stokes equations with delay on the convective term in bounded domain.Under appropriate assumption on the delay term,we establish the existence of pullback attractors for the fluid flow model,which is dependent on the past state.Inspired by the idea in Zelati and Gal’s paper(JMFM,2015),the robustness of pullback attractors has been proved via upper semi-continuity in last section.
基金The NNSF （10471084） of China and by Guangdong Provincial Natural Science Foundation（04010985）.
文摘Let S = {1,1/2,1/2^2,…,1/∞ = 0} and I = [0, 1] be the unit interval. We use ↓USC（S） and ↓C（S） to denote the families of the regions below of all upper semi-continuous maps and of the regions below of all continuous maps from S to I and ↓C0（S） = {↓f∈↓C（S） ： f（0） = 0}. ↓USC（S） endowed with the Vietoris topology is a topological space. A pair of topological spaces （X, Y） means that X is a topological space and Y is its subspace. Two pairs of topological spaces （X, Y） and （A, B） are called pair-homeomorphic （≈） if there exists a homeomorphism h ： X→A from X onto A such that h（Y） = B. It is proved that, （↓USC（S）,↓C0（S）） ≈（Q, s） and （↓USC（S）,↓C（S）／ ↓C0（S））≈（Q, c0）, where Q = [-1,1]^ω is the Hilbert cube and s = （-1,1）^ω,c0= {（xn）∈Q ： limn→∞= 0}. But we do not know what （↓USC（S）,↓C（S））is.
基金the Applied Research Project of Sichuan Province(05JY029-009-1)
文摘Let X, Y be two finite-dimensional topological vector spaces, Z a Hausdorff topological vector space, K C X and D C Z be two nonempty sets, C be a pointed, closed, and convex cone in Y with int C ≠θ Let S ： K → 2^K and T ： K → 2^D be two multivalued mappings, and φ ： K × D × K → Y be a trifunction. In this paper, we consider the generalized vector quasi-equilibrium problem, which is formulated by finding X∈ K and y∈ T（x） such that x∈ E S（x） and φ（x,y, u） （∈/） -int C for all u ∈ S（x）. We establish an existence result in which T is not supposed to have any continuity property. Our results extend and improve the corresponding results of Cubiotti, Yao and Guo.
文摘This paper is concerned with the existence and upper semi-continuity of random attractors for the nonclassical diffusion equation with arbitrary polynomial growth nonlinearity and multiplicative noise in H<sup>1</sup>(R<sup>n</sup>). First, we study the existence and uniqueness of solutions by a noise arising in a continuous random dynamical system and the asymptotic compactness is established by using uniform tail estimate technique, and then the existence of random attractors for the nonclassical diffusion equation with arbitrary polynomial growth nonlinearity. As a motivation of our results, we prove an existence and upper semi-continuity of random attractors with respect to the nonlinearity that enters the system together with the noise.
