摘要
利用拓扑度理论及不动点指数理论,讨论了渐近线性算子方程的四种类型的解(即零解、正解、负解和变号解)的存在性,并将这一抽象结果应用于微分方程两点边值问题.
In this paper, by using the topological degree theory and the fixed point index theory, the existence of four kinds of solutions （i.e., zero solution, positive solution, negative solution and sign-changing solution） for asymptotically linear operator equations is discussed, and the abstract results are applied to two-point boundary value problems for differential equations.
出处
《数学学报（中文版）》
SCIE
CSCD
北大核心
2007年第6期1403-1410,共8页
Acta Mathematica Sinica：Chinese Series
基金
国家自然科学基金(10671167
10471075)
关键词
不动点指数
变号解
正解
负解
fixed point index
positive solution
negative solution
sign-changing solution
