| 超线性Hammerstein积分方程的非零解 |
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| 引用本文： | 李福义,韩国栋.超线性Hammerstein积分方程的非零解[J].山西大学学报(自然科学版),2003,26(4):283-286. |
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| 作者姓名： | 李福义 韩国栋 |
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| 作者单位： | 山西大学,数学系,山西,太原,030006 |
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| 基金项目： | Shanxi Provincial Youth Science and Technique Foundation(2 0 0 2 10 0 1) |
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| 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Hammerstein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)5：528-537)的相关结果。
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| 关 键 词： | 超线性Hammerstein积分方程 非零解 锥理论 拓扑度 |
Existence of Non-zero Solutions to Nonlinear Hammerstein Integral Equation |
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| LI Fu-yi,HAN Guo-dong.Existence of Non-zero Solutions to Nonlinear Hammerstein Integral Equation[J].Journal of Shanxi University (Natural Science Edition),2003,26(4):283-286. |
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| Authors: | LI Fu-yi HAN Guo-dong |
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| Abstract: | 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. |
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| Keywords: | topological degree cone Hammerstein integral equation |
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