一类边值问题的三重正凹解

摘要

Consider the boundary value problem -u(6)(t)=f(u(t),-u″(t),u(4)(t)),t∈[0,1],u(0)=u′(1)=u″(0)=u(″′)(1)=u(4)(0)=u(4)(1)=0,where f≥0, the boundary conditions are different from the Lidstone boundary conditions.By using the Leggett-Williams Fixed Point Theroem,a sufficient condition for the existence of triple positive concave solutions of BVP is obtained.%研究边值问题-u(6)(t)=f(u(t),-u″(t),u(4)(t)),t∈[0,1],u(0)=u′(1)=0,u″(0)=u(″′)(1)=0,u(4)(0)=u(4)(1)=0,其中f≥0.其边值条件不同于Lidstone边值条件,应用Leggett-Williams不动点定理得到边值问题存在三重正解的充分条件.