In this paper, the global controllability for a class of high dimensional polynomial systems has been investigated and a constructive algebraic criterion algorithm for their global controllability has been obtained. B...In this paper, the global controllability for a class of high dimensional polynomial systems has been investigated and a constructive algebraic criterion algorithm for their global controllability has been obtained. By the criterion algorithm, the global controllability can be determined in finite steps of arithmetic operations. The algorithm is imposed on the coefficients of the polynomials only and the analysis technique is based on Sturm Theorem in real algebraic geometry and its modern progress. Finally, the authors will give some examples to show the application of our results.展开更多
In this paper, we discuss the inverse problem for indefinite Sturm-Liouville operators on the finite interval [a, b]. For a fixed index n（n = 0, 1, 2,… ）, given the weight function w（x）, we will show that the spe...In this paper, we discuss the inverse problem for indefinite Sturm-Liouville operators on the finite interval [a, b]. For a fixed index n（n = 0, 1, 2,… ）, given the weight function w（x）, we will show that the spectral sets {λn（q, ha,hk）}＋∞k=1 and {λ-n（q, hb,hk）}＋∞k=1 for distinct hk are sufficient to determine the potential q（x） on the finite interval [a, b] and coefficients ha and hb of the boundary conditions.展开更多
应用Leray-Schauder延拓定理,得到了二阶常微分方程多点边值问题x″(t)=f(t,x(t),x′(t))+e(t),t∈(0,1)αx(0)-βx′(0)=sum from i=1 to m-2 aix(ξi),γx(1)+δx′(1)=sum from j=1 to n-2 bjx(τj)解的存在性,其中f:[0,1]×R2→...应用Leray-Schauder延拓定理,得到了二阶常微分方程多点边值问题x″(t)=f(t,x(t),x′(t))+e(t),t∈(0,1)αx(0)-βx′(0)=sum from i=1 to m-2 aix(ξi),γx(1)+δx′(1)=sum from j=1 to n-2 bjx(τj)解的存在性,其中f:[0,1]×R2→R满足Caratheodory条件,e(.)∈L1(0,1),ai,bj∈R,ξi,τj∈(0,1),i=1,2,…,m-2,j=1,2,…,n-2,0<ξ1<ξ2<…<ξm-2<1,0<τ1<τ2<…<τn-2<1.展开更多
基金supported by the Natural Science Foundation of China under Grant Nos.60804008,61174048and 11071263the Fundamental Research Funds for the Central Universities and Guangdong Province Key Laboratory of Computational Science at Sun Yat-Sen University
文摘In this paper, the global controllability for a class of high dimensional polynomial systems has been investigated and a constructive algebraic criterion algorithm for their global controllability has been obtained. By the criterion algorithm, the global controllability can be determined in finite steps of arithmetic operations. The algorithm is imposed on the coefficients of the polynomials only and the analysis technique is based on Sturm Theorem in real algebraic geometry and its modern progress. Finally, the authors will give some examples to show the application of our results.
基金Supported by the National Natural Science Foundation of China(11171152)the Jiangsu Natural Science Foundation of China(BK2010489)
文摘In this paper, we discuss the inverse problem for indefinite Sturm-Liouville operators on the finite interval [a, b]. For a fixed index n（n = 0, 1, 2,… ）, given the weight function w（x）, we will show that the spectral sets {λn（q, ha,hk）}＋∞k=1 and {λ-n（q, hb,hk）}＋∞k=1 for distinct hk are sufficient to determine the potential q（x） on the finite interval [a, b] and coefficients ha and hb of the boundary conditions.
文摘应用Leray-Schauder延拓定理,得到了二阶常微分方程多点边值问题x″(t)=f(t,x(t),x′(t))+e(t),t∈(0,1)αx(0)-βx′(0)=sum from i=1 to m-2 aix(ξi),γx(1)+δx′(1)=sum from j=1 to n-2 bjx(τj)解的存在性,其中f:[0,1]×R2→R满足Caratheodory条件,e(.)∈L1(0,1),ai,bj∈R,ξi,τj∈(0,1),i=1,2,…,m-2,j=1,2,…,n-2,0<ξ1<ξ2<…<ξm-2<1,0<τ1<τ2<…<τn-2<1.
