四川师范大学学报（自然科学版）2011，Vol.34Issue(5)：646-650,5.DOI:10.3969/j.issn.1001-8395.2011.05.010
一类Hammerstein型积分方程的解
The Solutions of a Class of Hammerstein-type Integral Equations
摘要
Abstract
In this paper, by using the variational method, we discuss the existence of the solutions of a class of Hammeistein-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 toHeMBⅢKHH operatorfφ = f(x,φ(x) ) and using its quasiadditive property, the coerciviry 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 Frechet derivative A10' are obtained by related conclusions of topological degree and fixed point index.关键词
Hammerstein型积分方程/临界点/梯度算子/拓扑度/不动点Key words
Hammerstein-type integral equation/ critical point/ gradient operator/ topological degree/ fixed point分类
数理科学引用本文复制引用
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):646-650,5.基金项目
国家自然科学基金(10971179)和江苏省2010年研究生科研创新计划基金(CX10S-037Z)资助项目 （10971179）
