【作者】 吴克晴；

【导师】 李国祯；

【作者基本信息】 江西师范大学 ， 应用数学， 2004， 硕士

【摘要】 本文研究了某些非线性算子的不动点问题，获得了一些不动点定理。 第一章研究了随机混合单调算子的随机不动点问题，把[3]的一些混合单调算子不动点定理进行了随机化。 第二章研究了范围广泛的半闭1—集压缩算子，在e—连续的条件下把Amann三解定理进行了推广。 第三章运用文[9]无界集上的不动点指数去研究Banach空间无界集上的一些著名的边界条件以及固有值问题，获得无界集上相应的定理。 第四章运用文[9]无界集上半闭1-集压缩映象的不动点指数去研究半序Banach空间无界集上锥拉伸与锥压缩的问题，获得无界集上相应的定理。更多还原

【Abstract】 In this thesis, we investigate the fixed point problem of some nonlinear operators. And we gain some fixed point theorems.In chapter 1, we have studied random couple fixed points of nonlinear random mixed monotone operators ,and derived Some random version of Guo’s deterministic couple fixed point theorems for mixed monotone operators.In chapter 2, we have studied semi-closed 1-set contraction operators and generalized Amann’s three-solution theorem under the hypothesis of e-continuity.In chapter 3, by virtue of the index for semi-closed 1-set contraction mapping on the unbounded sets(see[9]), some well-known boundary conditions and proper value problems on bounded sets in Banach spaces are extended to the case that is on unbounded sets.In chapter 4, by virtue of the index for semi-closed 1-set contraction mapping on the unbounded sets(see[9]), the fixed point theorem of cone expansion and compression for semi-closed 1-set contraction mapping on an unbounded set is proved in semi-ordered Banach spaces.更多还原