摘要
该文利用拓扑方法讨论一类非线性Sturm-Liouville边值问题{-u″=λf(x,u),α_0u(0)+β_0u′(0)=0,α_1u(1)+β_1u′(1)=0;作者在非线性项不奇异和奇异两种情况下研究了上述问题正解解集的全局结构,在非线性项f不满足条件f(x,u)≥0(u≥0)时获得了正解的存在性.
In this paper, the following nonlinear Sturm-Liouville problem
{-u″=λf（x,u）,
α0u（0）＋β0u′（0）=0,α1u（1）＋β1u′（1）=0;
is discussed by topological methods. In the case that the nonlinear term is non-singular or singular, global structure of the positive solution set of the above problem is obtained, and the existence of positive solutions of the above problem is proved under the condition that the nonlinear term f（x, u） does not satisfy f（x, u） ≥ 0（u ≥ 0）.
出处
《数学物理学报（A辑）》
CSCD
北大核心
2008年第3期424-433,共10页
Acta Mathematica Scientia
基金
国家自然科学基金(10671167)资助
