奇异半正定二阶边值问题的正解存在性

Existence of positive solutions to singular second-order semi-positive definite boundary-value problems

借助于锥上的不动点指数理论研究奇异半正定二阶边值问题-x″(t)=f(t,x)(0<t<1),x(0)=x(1)=0的正解存在性.其中非线性项f可取负值且可没有下界,并且允许f在t=0,t=1,x=0处有很强奇异性的情形下,获得奇异半正定二阶边值问题的正解存在性.

By using the index theory of fixed point on a cone, the existence of positive solutions to secondorder singular semipositive definite boundary-value problem-x″f（t）=f（t,x） for 0〈t〈1, x（0）=x（1）=0 was studied. The nonlinear term f might take negative be allowed to have intensively singularity at t=0, t=1, and x=0 as well, and the existence of positive solution to this problem was verified in such a case.