摘要
考虑如下二阶Neumann边值问题:-u″+Mu=λf(t,u),0<t<1,u′(0)=u′(1)=0,其中,λ>0,M>0,f:(0,1]×(0,+∞)→(-∞,+∞)连续,f(t,u)允许在t=0,t=1处具有奇异性.在f无下界的条件下,利用锥压缩与拉伸不动点定理,讨论了二阶Neumann边值问题正解的存在性,改进和推广了现有f>0时的某些结果,并将所获得的结果应用于一个具体的二阶Neumann边值问题.
The existence of the following singular semipositone second-order Neumann BVP is discussed： -u＇＇＋Mu=λf（t,u）,0〈t〈1,u＇（0）=u＇（1）=0. Where λ〉0,M〉0,f：（0,1]×（0,＋∞）→（-∞,＋∞） is continuous, λ 〉 0 and M〉 0 is parameters, and f（t,u） may also be singular at t=0 or t=1. When f is unbounded below, the existence of positive solutions of singular semipositone second-order Neumann BVP is studied by means of fixed point theorem of conic expansion and compression of order type, and some results are improved and generalized when f〉0. And in the end,an example is given.
出处
《郑州大学学报（理学版）》
CAS
2006年第1期14-18,共5页
Journal of Zhengzhou University:Natural Science Edition
基金
郑州大学青年骨干教师资助计划课题
