Existence and Uniqueness of Positive Solution for Discrete Multipoint Boundary Value Problems
Keyword(s):
It is expected in this paper to investigate the existence and uniqueness of positive solution for the following difference equation: -Δ2u(t-1)=f(t, u(t))+g(t, u(t)), t∈Z1, T, subject to boundary conditions either u(0)-βΔu(0)=0, u(T+1)=αu(η) or Δu(0)=0, u(T+1)=αu(η), where 0<α<1, β>0, and η∈Z2,T-1. The proof of the main result is based upon a fixed point theorem of a sum operator. It is expected in this paper not only to establish existence and uniqueness of positive solution, but also to show a way to construct a series to approximate it by iteration.
2017 ◽
Vol 2017
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pp. 1-13
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2018 ◽
Vol 1
(1)
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pp. 21-36
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2009 ◽
Vol 2009
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pp. 1-15
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2007 ◽
Vol 2007
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pp. 1-10
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