Banach空间超线性算子方程的多解定理及其应用

Multiple Solutions for Superlinear Operator Equations in Banach Spaces and Applications

本文利用两对平行上下解,讨论了一类超线性算子方程的多解的存在性,得到了六解定理和七解定理.文中所得结果本质地改进了著名的Amann三解定理.作为应用,考虑了二阶微分方程组,得到了新的结论.

In this paper, existence of the multiple solutions for a kind of superlinear operator equations is discussed via two coupled parallel sub-super solutions. The results obtained in this paper essentially improve the famous Amann three-solution theorem. As applications, a second order system of differential equations is considered.