一类二阶奇异微分方程边值问题正解的存在性

The existence of positive solutions to boundary value problems for singular second order differential equations

研究一类二阶奇异微分方程(p(t)u′(t))′=q(t)f(u(t)),其中,f∈C(R+,R)有界。在满足边值条件u(′0)=0,u(M)=0下,应用临界点理论并结合分析的方法,证明了上述边值问题至少存在一个严格递减的正解。该结果推广了现有文献中的相关结论。

This paper deals with the existence of positive solutions to a class of singular second order differential euqation（p（t）u′（t））=q（t）f（u（t）） with boundary value condition u′（0）=0,u（M）=0,when f∈C（R＋,R） is bounded and p（0）=0.By combination of the critical point theory with mathematical analysis,some sufficient conditions are given to ensure that there exist at least one nontrivial decreasing positive solution to the above boundary value problems.These results generalize some corresponding results in the literature.