次线性半正边值问题的正解

Existence Results of Positive Solutions for Sublinear Semipositone Boundary Value Problems

中文关键词:  Sturm-Lionville边值问题  次线性  锥  全连续算子  正解存在性

英文关键词:Sturm-Liouville boundary value problem  sublinear  completely continuous operator  cone  existence of positive solution.

中文摘要:

      本文讨论 Sturm-Liouville边值问题(p(t)u′)′+λf(t,u)=0, r＜t＜R;au(r)-bp(r)u′(r)=0;cu(R)+dp(R)u′(R)=0,正解的存在性,这里允许非线性项取负值．当f在u=+∞处一致次线性增长且无界时，必存在λ^*＞0，对?λ:λ＞λ^*,上述边值问题存在正解．

英文摘要:

      We consider the existence of positive solutions for boundary value problems (p(t)u′)′+λf(t,u)=0, r＜t＜R;au(r)-bp(r)u′(r)=0;cu(R)+dp(R)u′(R)=0, where we allow that nonlinearity f(t,u) be negative. If f is sublinear at u=+∞ and unbounded, there exists a λ^*>0, the above boundary value problems has a positive solution for every λ＞λ^*.