@Article{CMR-34-221, author = {Lu , Yanqiong and Ma , Ruyun}, title = {Discrete ArzelĂ -Ascoli Theorem on the Half Line and Its Application}, journal = {Communications in Mathematical Research }, year = {2019}, volume = {34}, number = {3}, pages = {221--229}, abstract = {
The compactness criterion in
$
l_{\diamond}=\left\{x(\,\cdot\,)\in l^{\infty}(0,\infty))\mid\lim\limits_{t\rightarrow\infty}x(t)=x(\infty)\right\}
$
is given and as an application, we study the existence of positive solutions of second
order boundary value problems of difference equation on the half line by the fixed-point
theorem in cones.