Volume 34, Issue 3
Discrete Arzelà-Ascoli Theorem on the Half Line and Its Application

Commun. Math. Res., 34 (2018), pp. 221-229.

Published online: 2019-12

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• 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.

• Keywords

discrete Arzelà-Ascoli theorem, half line, positive solution, difference equation, fixed point

34G20

linmu8610@163.com (Yanqiong Lu)

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@Article{CMR-34-221, author = {Lu , Yanqiong and Ma , Ruyun}, title = {Discrete Arzelà-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.

}, issn = {2707-8523}, doi = {https://doi.org/10.13447/j.1674-5647.2018.03.04}, url = {http://global-sci.org/intro/article_detail/cmr/13483.html} }
TY - JOUR T1 - Discrete Arzelà-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 Arzelà-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.

Yanqiong Lu & Ruyun Ma. (2019). Discrete Arzelà-Ascoli Theorem on the Half Line and Its Application. Communications in Mathematical Research . 34 (3). 221-229. doi:10.13447/j.1674-5647.2018.03.04
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