| 一类Hammerstein型积分方程的解 |
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| 引用本文： | 李来,孙经先,赵吕慧子. 一类Hammerstein型积分方程的解[J]. 四川师范大学学报(自然科学版), 2011, 34(5): 646-650. DOI: 10.3969/j.issn.1001-8395.2011.05.010 |
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| 作者姓名： | 李来 孙经先 赵吕慧子 |
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| 作者单位： | 徐州师范大学数学科学学院,江苏徐州,221116 |
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| 基金项目： | 国家自然科学基金(10971179);江苏省2010年研究生科研创新计划基金(CX10S-037Z)资助项目 |
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| 摘 要： | 利用变分方法,在Hilbert空间中,研究了一类带正定核的Hammerstein型积分方程φ(x)=∫ck(x,y)f(y,φ(y))dy=Aφ解的存在性问题,通过对涅梅茨基算子fφ=f(x,φ(x))加条件,利用它的拟可加性,证明了泛函Φ(ψ)=1/2‖ψ‖ 2-ψ(Hψ)具有强制性,根据已有结论证明了泛函临界点的存...
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| 关 键 词： | Hammerstein型积分方程 临界点 梯度算子 拓扑度 不动点 |
The Solutions of a Class of Hammerstein-type Integral Equations |
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| LI Lai,SUN Jing-xian,ZHAO Lv-hui-zi. The Solutions of a Class of Hammerstein-type Integral Equations[J]. Journal of Sichuan Normal University(Natural Science), 2011, 34(5): 646-650. DOI: 10.3969/j.issn.1001-8395.2011.05.010 |
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| Authors: | LI Lai SUN Jing-xian ZHAO Lv-hui-zi |
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| Affiliation: | LI Lai,SUN Jing-xian,ZHAO Lv-hui-zi(Department of Mathematics,Xuzhou Normal University,Xuzhou 221116,Jiangsu) |
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| Abstract: | In this paper,by using the variational method,we discuss the existence of the solutions of a class of Hammerstein-type integral equations with positive kernel φ(x)=∫G k(x,y)f(y,φ(y))dy=Aφ in Hilbert spaces.By adding some conditions to Немвщкий operator fφ=f(x,φ(x)) and using its quasiadditive property,the coercivity of the function Φ(ψ)=1 2‖ ψ‖2-Ψ(Hψ) is obtained.Therefore,we prove the existence of critical points of the function,which is equivalent to the existence of the solutions of the integral equation.Moreover,the existences of fixed points of operator A1=H*fH and its Fréchet derivative A′1θ are obtained by related conclusions of topological degree and fixed point index. |
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| Keywords: | Hammerstein-type integral equation critical point gradient operator topological degree fixed point |
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