Discrete Arzelà-Ascoli Theorem on the Half Line and Its Application (Communications in Mathematical Research, 2019)
The compactness criterion in$l_{\diamond}=\left\{x(\,·\,)\in l^{∞}(0,∞))\mid\lim\limits_{t→∞}x(t)=x(∞)\right\}$is given and as an application, we study the existence of positive solutions of secondorder boundary value problems of difference equation on the half line by the fixed-pointtheorem in cones.
Keywords: discrete Arzelà-Ascoli theorem; half line; positive solution; difference equation; fixed point