TY - JOUR
T1 - Discrete ArzelĂ -Ascoli Theorem on the Half Line and Its Application
AU - Lu , Yanqiong
AU - Ma , Ruyun
JO - Communications in Mathematical Research
VL - 3
SP - 221
EP - 229
PY - 2019
DA - 2019/12
SN - 34
DO - http://doi.org/10.13447/j.1674-5647.2018.03.04
UR - https://global-sci.org/intro/article_detail/cmr/13483.html
KW - discrete ArzelĂ -Ascoli theorem, half line, positive solution, difference
equation, fixed point
AB - 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.