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外文期刊>Advances in Difference Equations
>Positive solutions of a discrete nonlinear third-order three-point eigenvalue problem with sign-changing Green’s function
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Positive solutions of a discrete nonlinear third-order three-point eigenvalue problem with sign-changing Green’s function
In this paper, by using the Krasnosel’skii fixed point theorem in a cone, we discuss the existence of positive solutions to the discrete third-order three-point boundary value problem { Δ 3 u ( t − 1 ) = λ a ( t ) f ( t , u ( t ) ) , t ∈ [ 1 , T − 2 ] Z , Δ u ( 0 ) = u ( T ) = Δ 2 u ( η ) = 0 , $$left { extstyleegin{array}{l} Delta^{3}u(t-1)=lambda a(t)f(t,u(t)), quad tin[1,T-2]_{mathbb{Z}}, Delta u(0)=u(T)=Delta^{2}u(eta)=0, end{array}displaystyle ight . $$ where T 4 $T4$ is an integer, [ 1 , T − 2 ] Z = { 1 , 2 , … , T −
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机译：在本文中，通过在锥体中使用Krasnosel'skii不动点定理，我们讨论了离散三阶三点边值问题{Δ3 u（t − 1）=λa（t ）f（t，u（t）），t∈[1，T-2] Z，Δu（0）= u（T）=Δ2 u（η）= 0，$$ left { textstyle begin {array} {l} Delta ^ {3} u（t-1）= lambda a（t）f（t，u（t））， quad t in [1，T-2] _ { mathbb {Z}}， Delta u（0）= u（T）= Delta ^ {2} u（ eta）= 0， end {array} displaystyle right。 $$，其中T> 4 $ T> 4 $是整数，[1，T − 2] Z = {1，2，…，T −
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