一类Hammerstein型积分方程的正解及其应用

ON POSITIVE SOLUTION OF SOME HAMMERSTEIN′S TYPE INTEGRAL EQUATIONS AND ITS APPLICATIONS

研究Ｈａｍｍｅｒｓｔｅｉｎ型积分方程的正解，其中，ｋ（ｘ，ｙ）≥０，ａ＿ｉ（ｘ）≥０，０＜ａ＿ｉ＜１（ｉ＝１，２，…，ｐ）对任意λ＞０，得到正解的存在唯一性与迭代算法，并且研究了作为λ的抽象函数的基本体质。把所得结果用于二阶非线性常微分方程边值问题。

The Hammerstein′s type integral cquation dywhere k(x,y )≥0 a_i(y)≥0,0<a_i<1,(i=1,2,…,p),is studied.The existence,unique.ness and iterative method of the positive solutions are obatined.Some fundamental propertiesof the which is abstract function on λare also studied.I.astly,the results are aplied to theboundary value problems for nonlinear sccond order ordinary differential equations.