Amann三解定理的改进及其应用

IMPROVEMENT ON AMANN'S THREE-SOLUTION THEOREM AND APPLICATIONS

本文对非线性泛函分析中著名的Ａｍａｎｎ三解定理作了本质性的改进，并将其结果应用到核函数不恒为正的Ｈａｍｍｅｒｓｔｅｉｎ型积分方程，得到了新的结论．

in this paper, we have improved the famous Amann's three--solution theorem[1,2]in nonlinear functional analysis, and have removed the forllwing conditions used by Amann:The cone is solid, the operator A is strongly increasing and A_e= A o Je|[u1,u2]e is a strict setcontraction. The improved Amann's three-solution theorem can be applied to Hammersteinintegral equations, where the kernel k(x, y) is not everywhere positive.