摘要
本文讨论 Sturm-Liouville边值问题（p（t）u’）’+λf（t,u）=0,r<t<Rau（r）-bp（r）u’（r）=0cu（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Vλ;λ>λ,上述边值问题存在正解.
We consider the existence of positive solutions for boundary value problems(p(t)u')'+λf(t, u) = 0, r<t<Rau(r) -bp(r)u'(r) = 0cu(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* .
基金
国家自然科学基金资助项目(19801028)
关键词
次线性
半正边值问题
正解
锥
全连续算子
Sturm-Liouville boundary value problem
sublinear
completely continuous operator
cone
existence of positive solution.
