In this paper,we get fixed point theorems of mixed monotone operators in much weaker condition and give some applications for nonmonotone operators and differential equations.
In this paper,the author proves the necessary and sufficient condition for the existence of 2-harmonically and isometrically immersed curves in a 2-dimensinonal surface N∪→IE^3.
In this paper, we study the optimal control problem of nonlinear differentialinclusions with principle operator being pseudomonotone. First, we give some propertiesof solutions of certain evolution equations. Further,...In this paper, we study the optimal control problem of nonlinear differentialinclusions with principle operator being pseudomonotone. First, we give some propertiesof solutions of certain evolution equations. Further, we prove the existence of admissibletrajectories for evolution inclusions. Then, we extend the Fillipov's selection theoremand discuss a general Lagrange type optimal control problem. Finally, we present anexample that demonstrates the appplicability of our results.展开更多
In this paper, the authors study reiterated homogenization of nonlinear equations of the form --div(a(x, x/ε x/ε, Duε) = f, where a is periodic in the first two arguments and monotone in the third. It is proved tha...In this paper, the authors study reiterated homogenization of nonlinear equations of the form --div(a(x, x/ε x/ε, Duε) = f, where a is periodic in the first two arguments and monotone in the third. It is proved that ue converges weakly in W1,P(Ω) (and even in some multiscale sense), as ε→ 0 to the solution uo of a limit problem. Moreover, an explicit expression for the limit problem is given. The main results were also stated in [15]. This article presents the complete proofs of these results.展开更多
The aim of this paper is to investigate the first Hochschild cohomology of ad- missible algebras which can be regarded as a generalization of basic algebras. For this purpose, the authors study differential operators ...The aim of this paper is to investigate the first Hochschild cohomology of ad- missible algebras which can be regarded as a generalization of basic algebras. For this purpose, the authors study differential operators on an admissible algebra. Firstly, dif- ferential operators from a path algebra to its quotient algebra as an admissible algebra ave discussed. Based on this discussion, the first cohomology with admissible algebras as coefficient modules is characterized, including their dimension formula. Besides, for planar quivers, the k-linear bases of the first cohomology of acyclic complete monomial algebras and acyclic truncated quiver algebras are constructed over the field k of characteristic 0.展开更多
The authors study homogenization of some nonlinear partial differential equations of the form -div (?(hx, h2x,Duh)) =f, where a is periodic in the first two arguments and monotone in the third. In particular the case ...The authors study homogenization of some nonlinear partial differential equations of the form -div (?(hx, h2x,Duh)) =f, where a is periodic in the first two arguments and monotone in the third. In particular the case where a satisfies degenerated structure conditions is studied. It is proved that uh converges weakly in W01,1 (?) to the unique solution of a limit problem as h ? '. Moreover, explicit expressions for the limit problem are obtained.展开更多
In this paper, a new existence theorem of anti-periodic solutions for a class ofstrongly nonlinear evolution equations in Banach spaces is presented. The equations contain nonlinear monotone operators and a nonmonoton...In this paper, a new existence theorem of anti-periodic solutions for a class ofstrongly nonlinear evolution equations in Banach spaces is presented. The equations contain nonlinear monotone operators and a nonmonotone perturbation. Moreover, throughan appropriate transformation, the existence of anti-periodic solutions for a class of secondorder nonlinear evolution equations is verified. Our abstract results are illustrated by anexample from quasi-linear partial differential equations with time anti-periodic conditionsand an example from quasi-linear anti-periodic hyperbolic differential equations.展开更多
文摘In this paper,we get fixed point theorems of mixed monotone operators in much weaker condition and give some applications for nonmonotone operators and differential equations.
文摘In this paper,the author proves the necessary and sufficient condition for the existence of 2-harmonically and isometrically immersed curves in a 2-dimensinonal surface N∪→IE^3.
基金Supported by the Natural Science Foundation of Guizhou university(200101007)
文摘In this paper, we study the optimal control problem of nonlinear differentialinclusions with principle operator being pseudomonotone. First, we give some propertiesof solutions of certain evolution equations. Further, we prove the existence of admissibletrajectories for evolution inclusions. Then, we extend the Fillipov's selection theoremand discuss a general Lagrange type optimal control problem. Finally, we present anexample that demonstrates the appplicability of our results.
文摘In this paper, the authors study reiterated homogenization of nonlinear equations of the form --div(a(x, x/ε x/ε, Duε) = f, where a is periodic in the first two arguments and monotone in the third. It is proved that ue converges weakly in W1,P(Ω) (and even in some multiscale sense), as ε→ 0 to the solution uo of a limit problem. Moreover, an explicit expression for the limit problem is given. The main results were also stated in [15]. This article presents the complete proofs of these results.
基金supported by the National Natural Science Foundation of China(Nos.11271318,11171296,11401522,J1210038)the Specialized Research Fund for the Doctoral Program of Higher Education of China(No.20110101110010)the Zhejiang Provincial Natural Science Foundation of China(No.LZ13A010001)
文摘The aim of this paper is to investigate the first Hochschild cohomology of ad- missible algebras which can be regarded as a generalization of basic algebras. For this purpose, the authors study differential operators on an admissible algebra. Firstly, dif- ferential operators from a path algebra to its quotient algebra as an admissible algebra ave discussed. Based on this discussion, the first cohomology with admissible algebras as coefficient modules is characterized, including their dimension formula. Besides, for planar quivers, the k-linear bases of the first cohomology of acyclic complete monomial algebras and acyclic truncated quiver algebras are constructed over the field k of characteristic 0.
文摘The authors study homogenization of some nonlinear partial differential equations of the form -div (?(hx, h2x,Duh)) =f, where a is periodic in the first two arguments and monotone in the third. In particular the case where a satisfies degenerated structure conditions is studied. It is proved that uh converges weakly in W01,1 (?) to the unique solution of a limit problem as h ? '. Moreover, explicit expressions for the limit problem are obtained.
基金This research is supported by the Science and Technology Committee of Guizhou Province,China(20023002)
文摘In this paper, a new existence theorem of anti-periodic solutions for a class ofstrongly nonlinear evolution equations in Banach spaces is presented. The equations contain nonlinear monotone operators and a nonmonotone perturbation. Moreover, throughan appropriate transformation, the existence of anti-periodic solutions for a class of secondorder nonlinear evolution equations is verified. Our abstract results are illustrated by anexample from quasi-linear partial differential equations with time anti-periodic conditionsand an example from quasi-linear anti-periodic hyperbolic differential equations.
