二阶差分方程周期边值问题正解集的全局结构

Global structure of solutions for periodic boundary value problem of second-order difference equation

运用区间分歧理论与拓扑度理论得到了二阶差分方程周期边值问题Δ2 u(t-1)-q(t)u(t)+λf(t,u(t))=0,t∈T,u(0)=u(T),u(1)=u(T+1)正解集的全局结构,其中T>1是一个整数,T={1,2,…,T},={1,2,…,T+1},λ∈[0,∞)是一个参数;q∈C(,[0,∞)),且对于任意的t 0∈,q(t 0)>0;f∈C(×[0,∞),[0,∞))且f(t,s)在s=0或无穷远处不能线性化.

The global structure of solutions for periodic boundary value problem of second-order difference equationΔ2 u(t-1)-q(t)u(t)+λf(t,u(t))=0,t∈T,u(0)=u(T),u(1)=u(T+1)is discussed by using the bifurcation theorems from an interval and topological degree theory,where T>1 is an integer,T={1,2,…,T},={1,2,…,T+1},λ∈[0,∞)is a parameter;q∈C(,[0,∞)),q(t 0)>0 for every t 0∈;f∈C(×[0,∞),[0,∞)),and f(t,s)are not necessarily linearizable for s near 0 or infinity.