超线性非线性Sturm-Liouville边值问题的正解

Positive Solutions of Superlinear Nonlinear Sturm-Liouville Boundary Value Problems

利用拓扑方法讨论了一类非线性Sturm-Liouville边值问题-u″=λf(x,u),0≤x≤1,α_0u(0)+β_0u′(0)=0,α_1u(1)+β_1u′(1)=0.研究了上述问题的正解的全局结构,在非线性项f(x,u)不满足条件f(x,u)≥0(u≥0)时获得了正解的存在性.

The following nonlinear Sturm-Liouville problem {-u″=λf（x,u）,0≤x≤1 a0u（0）＋βou′（0）=0,a1u（1）＋βou′（1）=0. is discussed by topological methods the above problem is obtained, and is proven under the condition that 0 （u 〉/0）. The global structure of the set of positive solutions to the existence of positive solutions of the above problem the nonlinear term f（x,u） does not satisfy f（x,u）≥0（u≥0）.