Positive Solutions of Second-order Difference Equation with Variable Coefficient on the Infinite Interval

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 problemsbegin{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, ninmathbb{N}, [0ex]alpha x(0)-betaDelta x(0)=0, quad limlimits_{nrightarrowinfty}x(n)=0end{array} right.end{align*}by the fixed point theorem in cones. The main results extend some results in the previous literature.