Multiple sclerosis(MS)is a chronic and incurable autoimmune neurodegenerative disease of the central nervous system.Although the symptoms of MS can be managed by vitamin D3 treatment alone,this condition cannot be com...Multiple sclerosis(MS)is a chronic and incurable autoimmune neurodegenerative disease of the central nervous system.Although the symptoms of MS can be managed by vitamin D3 treatment alone,this condition cannot be completely eradicated.Thus,there might be unknown factors capable of regulating the vitamin D receptor(VDR).Genome-wide analysis showed that miRNAs were associated with VDRs.We sought to determine the role and mechanism of action of miRNA-125a-5p and VDRs in a model of MS,mice with experimental autoimmune encephalomyelitis(EAE),which was induced by myelin oligodendrocyte glycoprotein 35–55 peptides.EAE mice showed decreased mean body weight but increased mean clinical scores compared with vehicle or control mice.And inflammatory infiltration was found in the lumbosacral spinal cord of EAE mice.In addition,VDR expression was significantly lower while the expression of miR-125a-5p was markedly higher in the spinal ventral horn of EAE mice than in vehicle or control mice.Importantly,activation of VDRs by paricalcitol or inhibition of miR-125a-5p by its antagomir markedly decreased the mean clinical scores in EAE mice.Interestingly,VDR and miR-125a-5p were co-localized in the same neurons of the ventral horn.More importantly,inhibition of miR-125a-5p remarkably blocked the decrease of VDRs in EAE mice.These results support a critical role for miR-125a-5p in modulating VDR activity in EAE and suggest potential novel therapeutic interventions.展开更多
The invariant sets and the solutions of the 1+2-dimensional generalized thin film equation are discussed. It is shown that there exists a class of solutions to the equations, which are invariant with respect to the se...The invariant sets and the solutions of the 1+2-dimensional generalized thin film equation are discussed. It is shown that there exists a class of solutions to the equations, which are invariant with respect to the set $$E_0 = \{ u:u_x = v_x F(u),u_y = v_y F(u)\} ,$$ where v is a smooth function of variables x, y and F is a smooth function of u. This extends the results of Galaktionov (2001) and for the 1+1-dimensional nonlinear evolution equations.展开更多
This paper deals with propagations of singularities in solutions to a parabolic system coupled with nonlocal nonlinear sources. The estimates for the four possible blow-up rates as well as the boundary layer profiles ...This paper deals with propagations of singularities in solutions to a parabolic system coupled with nonlocal nonlinear sources. The estimates for the four possible blow-up rates as well as the boundary layer profiles are established. The critical exponent of the system is determined also.展开更多
In the paper, we study the positive solutions of an elliptic system coming from a preypredator model with modified Leslie-Gower and Holling-Type II schemes. We study the existence, non-existence, bifurcation, uniquene...In the paper, we study the positive solutions of an elliptic system coming from a preypredator model with modified Leslie-Gower and Holling-Type II schemes. We study the existence, non-existence, bifurcation, uniqueness and stability of positive solutions. In particular, we obtain a continuum of positive solutions connecting a semitrivial solution to the unique positive solution of the limiting system.展开更多
This article concerns the existence of weak solutions of the first boundary value problem for a kind of strongly degenerate quasilinear parabolic equation in the anisotropic Sobolev Space. With the theory of anisotrop...This article concerns the existence of weak solutions of the first boundary value problem for a kind of strongly degenerate quasilinear parabolic equation in the anisotropic Sobolev Space. With the theory of anisotropic Sobolev spaces an existence result is proved.展开更多
In this paper the nonnegative classical solutions of a parabolic system with nonlinear boundary conditions are discussed. The existence and uniqueness of a nonnegative classical solution are proved. And some sufficien...In this paper the nonnegative classical solutions of a parabolic system with nonlinear boundary conditions are discussed. The existence and uniqueness of a nonnegative classical solution are proved. And some sufficient conditions to ensure the global existence and nonexistence of nonnegative classical solution to this problem are given. MR Subject Classification 35B40 - 35K55 Keywords nonnegative solution - blow up - nonlinear boundary conditions - parabolic system Supported by the Natural Science Foundation of the Education Department of Anhui Province (2001kj038zc).展开更多
In this paper, we investigate a prey-predator model with diffusion and ratio-dependent functional response subject to the homogeneous Neumann boundary condition. Our main focuses are on the global behavior of the reac...In this paper, we investigate a prey-predator model with diffusion and ratio-dependent functional response subject to the homogeneous Neumann boundary condition. Our main focuses are on the global behavior of the reaction-diffusion system and its corresponding steady-state problem. We first apply various Lyapunov functions to discuss the global stability of the unique positive constant steady-state. Then, for the steady-state system, we establish some a priori upper and lower estimates for positive steady-states, and derive several results for non-existence of positive non-constant steady-states if the diffusion rates are large or small.展开更多
We apply the imperfect bifurcation theory in Banach spaces to study the exact multiplicity of solutions to a perturbed logistic type equations on a symmetric spatial domain. We obtain the precise bifurcation diagrams.
In this article, we consider the existence of local and global solution to the Cauchy problem of a doubly nonlinear equation. By introducing the norms |||f||| h and 〈f〉h, we give the sufficient and necessary conditi...In this article, we consider the existence of local and global solution to the Cauchy problem of a doubly nonlinear equation. By introducing the norms |||f||| h and 〈f〉h, we give the sufficient and necessary conditions on the initial value to the existence of local solution of doubly nonlinear equation. Moreover some results on the global existence and nonexistence of solutions are considered.展开更多
We study finite time quenching for heat equations coupled via singular nonlinear boundary flux. A criterion is proposed to identify the simultaneous and non-simultaneous quenchings. In particular, three kinds of simul...We study finite time quenching for heat equations coupled via singular nonlinear boundary flux. A criterion is proposed to identify the simultaneous and non-simultaneous quenchings. In particular, three kinds of simultaneous quenching rates are obtained for different nonlinear exponent regions and appropriate initial data. This extends an original work by Pablo, Quirós and Rossi for a heat system with coupled inner absorption terms subject to homogeneous Neumann boundary conditions.展开更多
In this note, we prove the partial regularity of stationary weak solutions for the Landau- Lifshitz system with general potential in four or three dimensional space. As well known, in general, since the constraint of ...In this note, we prove the partial regularity of stationary weak solutions for the Landau- Lifshitz system with general potential in four or three dimensional space. As well known, in general, since the constraint of the methods, in order to get the partial regularity of stationary weak solution of the Landau-Lifshitz system with potential, we need to add some very strongly conditions on the potential. The main difficulty caused by potential is how to find the equation satisfied by the scaling function, which breaks down the blow-up processing. We estimate directly Morrey's energy to avoid the difficulties by blowing up.展开更多
基金supported by the International Science and Technology Cooperation Plan of Guizhou Province,China[(2013)7027]the National Natural Science Foundation of China(81471137 and 31730040).
文摘Multiple sclerosis(MS)is a chronic and incurable autoimmune neurodegenerative disease of the central nervous system.Although the symptoms of MS can be managed by vitamin D3 treatment alone,this condition cannot be completely eradicated.Thus,there might be unknown factors capable of regulating the vitamin D receptor(VDR).Genome-wide analysis showed that miRNAs were associated with VDRs.We sought to determine the role and mechanism of action of miRNA-125a-5p and VDRs in a model of MS,mice with experimental autoimmune encephalomyelitis(EAE),which was induced by myelin oligodendrocyte glycoprotein 35–55 peptides.EAE mice showed decreased mean body weight but increased mean clinical scores compared with vehicle or control mice.And inflammatory infiltration was found in the lumbosacral spinal cord of EAE mice.In addition,VDR expression was significantly lower while the expression of miR-125a-5p was markedly higher in the spinal ventral horn of EAE mice than in vehicle or control mice.Importantly,activation of VDRs by paricalcitol or inhibition of miR-125a-5p by its antagomir markedly decreased the mean clinical scores in EAE mice.Interestingly,VDR and miR-125a-5p were co-localized in the same neurons of the ventral horn.More importantly,inhibition of miR-125a-5p remarkably blocked the decrease of VDRs in EAE mice.These results support a critical role for miR-125a-5p in modulating VDR activity in EAE and suggest potential novel therapeutic interventions.
基金This work was supported by the National Natural Science Foundation of China (Grant No. 10671156)the Program for New Century Excellent Talents in Universities (Grant No. NCET-04-0968)
文摘The invariant sets and the solutions of the 1+2-dimensional generalized thin film equation are discussed. It is shown that there exists a class of solutions to the equations, which are invariant with respect to the set $$E_0 = \{ u:u_x = v_x F(u),u_y = v_y F(u)\} ,$$ where v is a smooth function of variables x, y and F is a smooth function of u. This extends the results of Galaktionov (2001) and for the 1+1-dimensional nonlinear evolution equations.
基金supported by the National Natural Science Foundation of China (Grant No. 10771024)
文摘This paper deals with propagations of singularities in solutions to a parabolic system coupled with nonlocal nonlinear sources. The estimates for the four possible blow-up rates as well as the boundary layer profiles are established. The critical exponent of the system is determined also.
基金supported by National Natural Science Foundation of China (Grant Nos. 10471022, 10771032)Natural Science Foundation of Jiangsu Province (Grant No. BK2006088)
文摘In the paper, we study the positive solutions of an elliptic system coming from a preypredator model with modified Leslie-Gower and Holling-Type II schemes. We study the existence, non-existence, bifurcation, uniqueness and stability of positive solutions. In particular, we obtain a continuum of positive solutions connecting a semitrivial solution to the unique positive solution of the limiting system.
基金The project is supported by NNSF of China (10371116)
文摘This article concerns the existence of weak solutions of the first boundary value problem for a kind of strongly degenerate quasilinear parabolic equation in the anisotropic Sobolev Space. With the theory of anisotropic Sobolev spaces an existence result is proved.
基金Supported by the Natural Science Foundation of the Education Department of Anhui Province( 2 0 0 1 kj0 38zc)
文摘In this paper the nonnegative classical solutions of a parabolic system with nonlinear boundary conditions are discussed. The existence and uniqueness of a nonnegative classical solution are proved. And some sufficient conditions to ensure the global existence and nonexistence of nonnegative classical solution to this problem are given. MR Subject Classification 35B40 - 35K55 Keywords nonnegative solution - blow up - nonlinear boundary conditions - parabolic system Supported by the Natural Science Foundation of the Education Department of Anhui Province (2001kj038zc).
基金the National Natural Science Foundation of China (Grant Nos. 10801090, 10726016,10771032)the Scientific Innovation Team Project of Hubei Provincial Department of Education (Grant No.T200809)
文摘In this paper, we investigate a prey-predator model with diffusion and ratio-dependent functional response subject to the homogeneous Neumann boundary condition. Our main focuses are on the global behavior of the reaction-diffusion system and its corresponding steady-state problem. We first apply various Lyapunov functions to discuss the global stability of the unique positive constant steady-state. Then, for the steady-state system, we establish some a priori upper and lower estimates for positive steady-states, and derive several results for non-existence of positive non-constant steady-states if the diffusion rates are large or small.
基金the National Natural Science Foundation of China (Grant No. 10671049), Longjiang Scholar GrantScience Research Fund of the Education Department of Heilongjiang Province (Grant No.11531246)Harbin Normal University Academic Backbone of Youth Project
文摘We apply the imperfect bifurcation theory in Banach spaces to study the exact multiplicity of solutions to a perturbed logistic type equations on a symmetric spatial domain. We obtain the precise bifurcation diagrams.
基金the National Natural Science Foundation of China (Grant No. 10531020)
文摘In this article, we consider the existence of local and global solution to the Cauchy problem of a doubly nonlinear equation. By introducing the norms |||f||| h and 〈f〉h, we give the sufficient and necessary conditions on the initial value to the existence of local solution of doubly nonlinear equation. Moreover some results on the global existence and nonexistence of solutions are considered.
基金supported by the National Natural Science Foundation of China (Grant No. 10471013, 10771024)
文摘We study finite time quenching for heat equations coupled via singular nonlinear boundary flux. A criterion is proposed to identify the simultaneous and non-simultaneous quenchings. In particular, three kinds of simultaneous quenching rates are obtained for different nonlinear exponent regions and appropriate initial data. This extends an original work by Pablo, Quirós and Rossi for a heat system with coupled inner absorption terms subject to homogeneous Neumann boundary conditions.
基金supported by National Natural Science Foundation of China (Grant Nos. 10631020, 60850005)the Natural Science Foundation of Zhejiang Province (Grant No. D7080080)
文摘In this note, we prove the partial regularity of stationary weak solutions for the Landau- Lifshitz system with general potential in four or three dimensional space. As well known, in general, since the constraint of the methods, in order to get the partial regularity of stationary weak solution of the Landau-Lifshitz system with potential, we need to add some very strongly conditions on the potential. The main difficulty caused by potential is how to find the equation satisfied by the scaling function, which breaks down the blow-up processing. We estimate directly Morrey's energy to avoid the difficulties by blowing up.
