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
在讨论非线性Hammerstein型积分方程(*)φ(x)=integral from n=G to k(x,y)f(y,φ(y))dy,0<mesG<+∞时证明了:当f(x,u)满足文中假设(ii)—(iv)时,方程(*)具有三个互异解。作为其应用,还讨论了非线性Sturm-Liourille问题(**)d^2u/(...在讨论非线性Hammerstein型积分方程(*)φ(x)=integral from n=G to k(x,y)f(y,φ(y))dy,0<mesG<+∞时证明了:当f(x,u)满足文中假设(ii)—(iv)时,方程(*)具有三个互异解。作为其应用,还讨论了非线性Sturm-Liourille问题(**)d^2u/(dx^2)+f(x,u)=0,au(0)+bu'(0)=0,cu(1)+du'(1)=0,得到问题(**)三个互异C^2类解的存在性。本文使用变分方法,主要结果的证明基于文[1]中建立的“等”高”山路定理。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.
文摘在讨论非线性Hammerstein型积分方程(*)φ(x)=integral from n=G to k(x,y)f(y,φ(y))dy,0<mesG<+∞时证明了:当f(x,u)满足文中假设(ii)—(iv)时,方程(*)具有三个互异解。作为其应用,还讨论了非线性Sturm-Liourille问题(**)d^2u/(dx^2)+f(x,u)=0,au(0)+bu'(0)=0,cu(1)+du'(1)=0,得到问题(**)三个互异C^2类解的存在性。本文使用变分方法,主要结果的证明基于文[1]中建立的“等”高”山路定理。
