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Positive solutions to nonlinear second-order three-point boundary-value problems for difference equation with change of sign

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Author(s): Chunli Wang | Xiaoshuang Han | Xiaoshuang Li

Journal: Electronic Journal of Differential Equations
ISSN 1072-6691

Volume: 2008;
Issue: 87;
Start page: 1;
Date: 2008;
Original page

Keywords: Boundary value problem | positive solution | difference equation | fixed point | changing sign coefficients

ABSTRACT
In this paper we investigate the existence of positive solution to the discrete second-order three-point boundary-value problem $$displaylines{ Delta^2 x_{k-1}+ h(k) f(x_k)=0, quad k in [1, n], cr x_0 =0, quad a x_l = x_{n+1}, }$$ where $n in [2, infty)$, $l in [1, n]$, $0 < a < 1$, $(1-a)l geq 2$, $(1+a)lleq n+1$, $f in C(mathbb{R}^+,mathbb{R}^+)$ and $h(t)$ is a function that may change sign on $[1, n]$. Using the fixed-point index theory, we prove the existence of positive solution for the above boundary-value problem.
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