M-PN空间中非线性算子方程解的存在性问题  

Existence for Solution of Nonlinear Operator Equation Problems in M-PN Space

作　　者：朱传喜[1] 王圣[1] 

机构地区：[1]南昌大学数学系,江西南昌330031

出　　处：《南昌大学学报（工科版）》2008年第1期16-18,共3页Journal of Nanchang University(Engineering & Technology)

基　　金：国家自然科学基金资助项目(10461007;10761007);江西省自然科学基金资助项目(0411043;2007GZS2051);江西省教育厅科研资助项目(2006[8])

摘　　要：利用概率线性赋范空间中的Leray-Schauder拓扑度理论,通过改变算子所满足的边界条件,研究了非线性算子方程Tx=Lx和Tx-Lx+p的解的存在性问题,在不要求方程满足L≥1的条件下(在文[1,2]中都要求方程满足条件L≥1),得到了几个新的定理.同时改进了文[1]中关于非线性算子方程Tx=μx(μ≥1)的结论,并且推广文[2]中关于非线性算子方程Tx=Lx+p(L≥1)的结论。Utilizing laray-schauder topological degree theorems in menger PN space and with the diversification of bounding conditions that the operators should hold, the existence of the solution of nonlinear operator equations Tx = Lx and Tx = Lx ＋ p are studied. Some new theorems without condition L ≥ 1 of equation （ In [ 1, 2 ] , equations must be satisfied this condition） is obtained. Meanwhile, the results in [ 1 ] for nonlinear operator equation Tx =μx （μ≥〉1） are the improved and the results in [ 2] for nonlinear operator equation Tx=Lx（L≥1） are generalized.

关 键 词：M-PN空间 拓扑度 同伦不变性 紧连续算子 

分 类 号：O211.3[理学—概率论与数理统计] O177.91[理学—数学]