Existence of Positive Solutions for a Discrete Three-Point Boundary Value Problem

Huting Yuan, Guang Zhang and Hongliang Zhao

Discrete Dynamics in Nature and Society, 2007, vol. 2007, 1-14

Abstract:

A discrete three-point boundary value problem Δ 2 x k − 1 + λ f k ( x k ) = 0 , k = 1 , 2 , … , n ,  x 0 = 0 , a x l = x n + 1 , is considered, where 1 ≤ l ≤ n is a fixed integer, a is a real constant number, and λ is a positive parameter. A characterization of the values of λ is carried out so that the boundary value problem has the positive solutions. Particularly, in this paper the constant a can be negative numbers. The similar results are not valid for the three-point boundary value problem of differential equations.

Date: 2007
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnddns:049293

DOI: 10.1155/2007/49293

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