摘要
本文考虑带非负系数矩阵的非线性代数系统Bu=f(u).当f在∞是次线性增长,在o点具有某种奇异性,以及f在∞和0都是超线性增长的情形下,利用初等变分法建立了系统存在正解和负解的若干充分条件.这些条件是"sharp"的并且结论是新的.本文的定理4还放宽了已有文献对矩阵B的限制.此外,我们给出一些例子说明本文结论的应用.
In this paper we consider the nonlinear algebra system Bu=f（u）, where B is a non-negative matrix, f is subquadratic near ∞ and has some singularity at 0, or f is superquadratic near ∞ and 0. By means of the elementary variational approach, we estab- lish some sufficient conditions which insure the existence of positive solutions and negative solution of this system. Such conditions are ＂sharp＂ and our conclusions are new. The Theorem 4 of this paper also relax the restrictions on the the matrix B in the literature. Some examples are given to illustrate our main results.
出处
《应用数学学报》
CSCD
北大核心
2015年第1期137-149,共13页
Acta Mathematicae Applicatae Sinica
基金
国家自然科学基金(11201086)
广东高校优秀青年创新人才培养计划项目(2012LYM_0087)
广东省高等学校优秀青年教师培养计划(yq2013107)资助项目
关键词
非线性代数系统
正解
初等变分法
nonlinear algebra system
positive solutions
elementary variational approach.
