摘要：Consider positive solutions and multiple positive solutions for a discrete nonlinear third-order boundary value problem { Δ 3 u ( t − 1 ) = a ( t ) f ( t , u ( t ) ) , t ∈ [ 1 , T − 2 ] Z , Δ u ( 0 ) = u ( T ) = 0 , Δ 2 u ( η ) − α Δ u ( T − 1 ) = 0 , $$ \textstyle\begin{cases} \Delta ^"u(t-1)=a(t)f(t,u(t)), \quad t\in [1,T-2]_{\mathbb{Z}},\\ \Delta u(0)=u(T)=0,\qquad \Delta ^, u(\eta )-\alpha \Delta u(T-1)=0, \end{cases} $$ which has the sign-changing Green’s function. Here T > 8 $T>8$ is a positive integer, [ 1 , T − 1 ] Z = { 1 , 2 , … , T − 2 } $[1,T-1]_{\mathbb{Z}}=\{1,2,\dots ,T-2\}$ , α ∈ [ 0 , 1 T − 1 ) $\alpha \in [0, \frac){T-1})$ , a : [ 0 , T − 2 ] Z → ( 0 , + ∞ ) $a:[0,T-2]_{\mathbb{Z}}\to (0,+\infty )$ , f : [ 1 , T − 2 ] Z × [ 0 , ∞ ) → [ 0 , ∞ ) $f:[1,T-2]_{ \mathbb{Z}}\times [0,\infty )\to [0,\infty )$ is continuous.
关键词：Discrete third-order three-point boundary value problem ; Positive solutions ; Cone ; Fixed point ; Sign-changing Green’s function
