超线性 Hammerstein积分方程的非零解(英文)  

Existence of Non-zero Solutions to Nonlinear Hammerstein Integral Equation

作　　者：李福义[1] 韩国栋[1] 

机构地区：[1]山西大学数学系,山西太原030006

出　　处：《山西大学学报（自然科学版）》2003年第4期283-286,共4页Journal of Shanxi University(Natural Science Edition)

基　　金：Shanxi Provincial Youth Science and Technique Foundation(2 0 0 2 10 0 1)

摘　　要：利用锥理论来计算算子 I- A的拓扑度 ,得到了一个一般性定理 ,并应用该定理讨论了非线 Ham merstein积分方程 ,得到了该方程存在非零解的一个充分条件 ,其中不要求算子 A映锥到自身 .所得结果不要求非线性算子F有下界 ,所以改进了孙经先 (数学年刊 ,1986 ,7(A) 5 :5 2 8- 5 37)的相关结果 .Using the theory of cone to calculate the topological degree of operator I-A,a general theorem was established.As an application of the theorem,the nonlinear Hammerstein integral equation was considered and a sufficient condition for the existence of the non-zero solution of the equation was obtained,where the operator A needn't maps the cone to itself .Since the nonlinear operator F neednt't be lower bounded,the results in this paper extend and improve the corresponding results of Sun in China Ann.of Math,1986,7A(5):528-537.

关 键 词：超线性Hammerstein积分方程 非零解 锥理论 拓扑度 

分 类 号：O175.5[理学—数学] O241.83[理学—基础数学]