二阶离散周期边值问题的多重正解

Muitiple Positive Solutions to Second-order Discrete Periodic Boundary

考虑如下边界值问题:-Δ[p(n-1)Δy(n-1)]+q(n)y(n)=f(n,y(n)),n∈[1,N](1.1)y(0)=y(N),p(0)Δy(0)=p(N)Δy(N)(1.2)其中{y(n)}nN=+01是一个期望解.运用锥不动点定理,给出了一种二阶离散周期边值问题多重正解的新的存在性定理.

we consider the following periodic boundary value problem：-Δ[p（n-1）Δy（n-1）]＋q（n）y（n）=f（n,y（n））,n∈[1,N]（1.1） y（0）=y（N）,p（0）Δy（0）=p（N）Δy（N）（1.2） where {y（n）}n=0^N＋1 is a desired solution, we present a new existence theory for muitiple positive solutions to a kind of second-order discrete periodic boundary value problems by employing a fixed point theorem in cones.