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| Positive Solutions of Second-order Difference Equation with Variable Coefficient on the Infinite Interval |
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| KeyWord:Positive solution Green's function Compact Infinite interval |
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| Abstract: |
| In this paper, based on the one-signed Green's function and the compact results on the infinite interval, we obtain the existence and multiplicity of positive solutions for the boundary value problems
\begin{align*}
\left\{\begin{array}{ll}
\Delta^2x(n-1)-p(n)\Delta x(n-1)-q(n)x(n-1)+f(n,x(n))=0, \ n\in\mathbb{N}, \\[0ex]
\alpha x(0)-\beta\Delta x(0)=0, \quad \ \ \lim\limits_{n\rightarrow\infty}x(n)=0
\end{array} \right.
\end{align*}
by the fixed point theorem in cones. The main results extend some results in the previous literature. |
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