奇异二阶Neumann边值问题的正解

Positive solutions of singular second-order Neumann boundary value problems

考察非线性二阶边值问题-u″(t)+λu(t)=h(t)f(t,u(t))+ζ(t,u(t)),0<t<1,u′(0)=u′(1)=0,的正解,其中λ>0.文中允许ζ(t,u)在t=0,t=1和u=0处奇异.利用锥上的GuoKrasnosel'skii不动点定理证明了n个正解的存在性,其中n是任意的正整数.

Letλ0.The positive solutions are considered for the nonlinear second-order Neumann boundary value problem -u＂（t） ＋λu（t） = h（t）f（t,u（t））＋ξ（t,u（t））,0t1,u＇（0） =u＇（1） = 0. Hereξ（t,u） is allowed to be singular at t = 0,t = 1 and u = 0.By applying the Guo-Krasnosel＇skii fixed point theorem on cone,the existence of n positive solutions is proved,where n is an arbitrary positive integer.