一类高阶微分方程边值问题正解的存在性

Positive solutions for higher order ordinary differential equation with boundary

假设m2<(2n-1)(n-1)!f、(x,u)在[0,1]×[0,∞)非负连续,利用锥拉伸与压缩不动点定理证明了高阶微分方程边值问题u(n)+m2u+f(x,u)=0,u(k)(0)=u(1)=0,0≤k≤n-2正解的存在性。

The existence of positive solutions for higher order ordinary differential boundary with value problem as u^（n） ＋ m^2u ＋f（x, u） =0, u^（k）（0） = u（1） = 0,0≤ k≤ n - 2 was proven when m^2 〈 （2n - 1） （ n - 1 ） ! and f（ x, u） is non - negative consecutive. The positive solutions for higher order ordinary differential boundary with value problem were solved on the basis of the cone- fixed point theorem.