二阶奇异周期边值问题正解的存在性和多重性

Multiplicity and Existence of Positive Solutions for Second-Order Singular Periodic Boundary Value Problems

研究了二阶奇异周期边值问题u(″t)+a(t)u(t)=f(t,u(t)),t∈[0,ω],u(0)=u(ω),u(′0)=u′(ω)正解的存在性,当允许f(t,u)在u=0和u=c(c>0)同时奇异时,用锥映射的Krasnoselsk ii不动点定理获得了其正解的存在性和多重性结果.

The existence of positive solutions for a second order singular Periodic Boundary Value Problemu（″t）＋a（t）u（t）=f（t,u（t））,t∈[0,ω],u（0）=u（ω）,u（′0）=u′（ω）is discussed. Here,f（t,u） may be singular at u =0 and u =c（c 〉0） ,By using Krasnoselskii fixed point theorem of cone map, some existence and multiplicity result of positive solutions are obtained.