Let G be a finitely generated torsion-free nilpotent group and a an automorphism of prime order p of G. If the map ψ ： G → G defined by g^φ = [g, α] is surjective, then the nilpotent class of G is at most h（p）,...Let G be a finitely generated torsion-free nilpotent group and a an automorphism of prime order p of G. If the map ψ ： G → G defined by g^φ = [g, α] is surjective, then the nilpotent class of G is at most h（p）, where h（p） is a function depending only on p. In particular, if α^3 = 1, then the nilpotent class of G is at most 2.展开更多
Based on the classical(matrix type)input-output analysis,a type of nonlinear (continuous type) conditional Leontief model,input-output equation were introduced,as well as three corresponding questions,namely,solvabili...Based on the classical(matrix type)input-output analysis,a type of nonlinear (continuous type) conditional Leontief model,input-output equation were introduced,as well as three corresponding questions,namely,solvability,continuity and surjectivity,and some fixed point and surjectivity methods in nonlinear analysis were used to deal with these questions. As a result,the main theorems are obtained,which provide some sufficient criterions to solve above questions described by the boundary properties of the enterprises consuming operator.展开更多
The main purpose of this paper is to study the surjectivity theorems for maximal monotone mapping in reflexive Banach spaces by using fixed point theory. We prove some new surjectivity theorems under some conditions a...The main purpose of this paper is to study the surjectivity theorems for maximal monotone mapping in reflexive Banach spaces by using fixed point theory. We prove some new surjectivity theorems under some conditions and give its application in differential equation.展开更多
This is the first part of a work on second order nonlinear, nonmonotone evolution inclusions defined in the framework of an evolution triple of spaces and with a multivalued nonlinearity depending on both x（t） and x...This is the first part of a work on second order nonlinear, nonmonotone evolution inclusions defined in the framework of an evolution triple of spaces and with a multivalued nonlinearity depending on both x（t） and x（t）. In this first part we prove existence and relaxation theorems. We consider the case of an usc, convex valued nonlinearity and we show that for this problem the solution set is nonempty and compact in C^1 （T, H）. Also we examine the Isc, nonconvex case and again we prove the existence of solutions. In addition we establish the existence of extremal solutions and by strengthening our hypotheses, we show that the extremal solutions are dense in C^1 （T, H） to the solutions of the original convex problem （strong relaxation）. An example of a nonlinear hyperbolic optimal control problem is also discussed.展开更多
Letϕ:Pc(M1)→Pc(M2)be a surjective Lp-isometry between Grassmann spaces of projections with the trace value c in semifinite factors M1 and M2.Based on the characterization of surjective Lp-isometries of unitary groups...Letϕ:Pc(M1)→Pc(M2)be a surjective Lp-isometry between Grassmann spaces of projections with the trace value c in semifinite factors M1 and M2.Based on the characterization of surjective Lp-isometries of unitary groups in finite factors,we show thatϕor I−ϕcan be extended to a∗-isomorphism or a∗-antiisomorphism.In particular,ϕis given by a∗-(anti-)isomorphism unless M1 and M2 are finite and c=12.展开更多
This paper shows that if a Gateaux differentiable functional f has a finite lower bound(although it need not attain it),then,for everyε>0,there exists some point zεsuch that‖f′(zε)‖ε1+h(‖zε‖),where h:[0,...This paper shows that if a Gateaux differentiable functional f has a finite lower bound(although it need not attain it),then,for everyε>0,there exists some point zεsuch that‖f′(zε)‖ε1+h(‖zε‖),where h:[0,∞)→[0,∞)is a continuous function such that∫∞011+h(r)dr=∞.Applications are given to extremum problem and some surjective mappings.展开更多
Suppose that f:Hn → Hn (n≥2) maps any r-dimensional hyperplane (1≤r【n) into an r-dimensional hyperplane. In this paper, we prove that f is an isometry if and only if f is a surjective map. This result gives an aff...Suppose that f:Hn → Hn (n≥2) maps any r-dimensional hyperplane (1≤r【n) into an r-dimensional hyperplane. In this paper, we prove that f is an isometry if and only if f is a surjective map. This result gives an affirmative answer to a recent conjecture due to Li and Yao.展开更多
基金The NSF(11371124)of Chinathe NSF(F2015402033)of Hebei Provincethe Doctoral Special Foundation(20120066)of Hebei University of Engineering
文摘Let G be a finitely generated torsion-free nilpotent group and a an automorphism of prime order p of G. If the map ψ ： G → G defined by g^φ = [g, α] is surjective, then the nilpotent class of G is at most h（p）, where h（p） is a function depending only on p. In particular, if α^3 = 1, then the nilpotent class of G is at most 2.
文摘Based on the classical(matrix type)input-output analysis,a type of nonlinear (continuous type) conditional Leontief model,input-output equation were introduced,as well as three corresponding questions,namely,solvability,continuity and surjectivity,and some fixed point and surjectivity methods in nonlinear analysis were used to deal with these questions. As a result,the main theorems are obtained,which provide some sufficient criterions to solve above questions described by the boundary properties of the enterprises consuming operator.
基金Foundation item： Supported by the Shanxi Gaoxiao Keji Kaifa Yanjiu（2007129） Supported by Boshi Ke yan Qidong Jijin of Shanxi University of Finance and Economics（2006） Supported by the Natural Science Foundation of Shanxi Province（2008011002-3）.Acknowledgment The authors wish to express thanks to referees for valuable suggestions.
文摘The main purpose of this paper is to study the surjectivity theorems for maximal monotone mapping in reflexive Banach spaces by using fixed point theory. We prove some new surjectivity theorems under some conditions and give its application in differential equation.
文摘This is the first part of a work on second order nonlinear, nonmonotone evolution inclusions defined in the framework of an evolution triple of spaces and with a multivalued nonlinearity depending on both x（t） and x（t）. In this first part we prove existence and relaxation theorems. We consider the case of an usc, convex valued nonlinearity and we show that for this problem the solution set is nonempty and compact in C^1 （T, H）. Also we examine the Isc, nonconvex case and again we prove the existence of solutions. In addition we establish the existence of extremal solutions and by strengthening our hypotheses, we show that the extremal solutions are dense in C^1 （T, H） to the solutions of the original convex problem （strong relaxation）. An example of a nonlinear hyperbolic optimal control problem is also discussed.
基金supported by the Science and Technology Research Program of Chongqing Municipal Education Commission(Grant No.KJQN2021000529)the Natural Science Foundation of Chongqing Science and Technology Commission(Grant No.cstc2020jcyj-msxm X0723)+2 种基金supported by Young Talent Fund of University Association for Science and Technology in Shaanxi(Grant No.20210507)supported by National Natural Science Foundation of China(Grant Nos.11871127and 11971463)supported by National Natural Science Foundation of China(Grant Nos.11971463,11871303 and 11871127)。
文摘Letϕ:Pc(M1)→Pc(M2)be a surjective Lp-isometry between Grassmann spaces of projections with the trace value c in semifinite factors M1 and M2.Based on the characterization of surjective Lp-isometries of unitary groups in finite factors,we show thatϕor I−ϕcan be extended to a∗-isomorphism or a∗-antiisomorphism.In particular,ϕis given by a∗-(anti-)isomorphism unless M1 and M2 are finite and c=12.
文摘This paper shows that if a Gateaux differentiable functional f has a finite lower bound(although it need not attain it),then,for everyε>0,there exists some point zεsuch that‖f′(zε)‖ε1+h(‖zε‖),where h:[0,∞)→[0,∞)is a continuous function such that∫∞011+h(r)dr=∞.Applications are given to extremum problem and some surjective mappings.
基金supported by National Natural Science Foundation of China (Grant No.10771059)Tianyuan Foundation
文摘Suppose that f:Hn → Hn (n≥2) maps any r-dimensional hyperplane (1≤r【n) into an r-dimensional hyperplane. In this paper, we prove that f is an isometry if and only if f is a surjective map. This result gives an affirmative answer to a recent conjecture due to Li and Yao.
