一类非线性二阶离散三点边值问题正解的全局结构

本文研究非线性二阶差分方程三点边值问题■正解的全局结构,其中Δu(t)=u(t+1)-u(t),Δ~2u(t)=Δ(Δu(t))=u(t+2)-2u(t+1)+u(t),T≥4为整数,η∈{1,2,…,T-1},λ∈0,1)为参数,函数f∈C(0,∞),0,∞))且f(s)0,s0,h:{1,2,…,T-1}→0,∞)且在{1,2,…,T-1}的任一非空子集上不恒为零.在非线性项f分别满足超线性增长和次线性增长的条件下,本文运用锥上的不动点指数理论及解集的连通性质获得了该问题正解的全局结构.

Global structure of positive solutions for a class of nonlinear second-order discrete three-point boundary value problems

In this paper, we study the global structure of positive solutions for a class of nonlinear second-order difference equation with three-point boundary value problems. Applying the fixed point index theory on cone and connectivity properties of the solution set, the global structure of positive solutions is obtained under the conditions that the nonlinear term satisfies the superlinear growth and the sublinear growth respectively.