关于一类Diophantus方程sum from i=1 to n (xi)=пmultiply from i=1 to n (xi)的整解

作者在本文中 ,引入了解型概念 ,并将解型分为平凡、正、负、0 -混合及非 0 -混合五种 ,从而极大地降低了问题的复杂性 ,得到了两个关键定理 (定理 4以及定理 1 0 )提供了求 Diophantus方程∑ni=1xi= ni=1xi 的全部正解型及全部非 0 -混合解型的途径。从而 ,解决了这两种解型的个数及构造问题。

NONTRIVIAL SOLUTIONS FOR A CLASS OF NON-DIVERGENCE EQUATIONS ON POLARIZABLE CARNOT GROUP

Some new properties of polarizable Carnot group are given.By choosing a proper constant a nontrivial solution of a class of non-divergence Dirichlet problem on the polarizable Carnot group is constructed.Thus the multi-solution property of corresponding non-homogeneous Dirichlet problem is proved and the best possible of LQ norm in the famous Alexandrov-Bakelman-Pucci type estimate is discussed.