二阶奇异边值问题两个非负解的存在性

THE EXISTENCE OF NONNEGATIVE SOLUTIONS OF SECOND ORDER SINGULAR BOUNDARY VALUE PROBLEM

利用拓扑度理论，给出了边值问题ｕ″（ｔ）＋λａ（ｔ）ｆ（ｕ（ｔ））＝０，０＜ｔ＜１，αｕ（０）－βｕ′（０）＝０，γｕ（１）＋δｕ′（１）＝０两个非负解的存在性结果，这里允许ａ在ｔ＝０和ｔ＝１处有奇性．当ｆ在０点超线性增长而在＋∞处次线性增长时，必存在σ＞０，对σ＜λ＜＋∞时，上述问题至少有两个不恒为零的非负解．

Using topological degree theory, we obtain existence of nonnegative solutions of singular boundary value problem u″(t)+λa(t)f(u(t))=0, 0<t<1 αu(0)-βu′(0)=0, γu(1)+δu′(1)=0, where a may be singular at both end points t =0 and t =1. If f is suplinear at u =0 and f is sublinear at u=+∞, there must exist positive number σ , for σ<λ<+∞, the above problem have at least two unidentically vanishing nonnegative solutions.