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

Yanqiong Lu & Ruyun Ma

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

  • AMS Subject Headings

34G20

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

linmu8610@163.com (Yanqiong Lu)

  • BibTex
  • RIS
  • TXT
@Article{CMR-34-221, author = {Yanqiong and Lu and linmu8610@163.com and 5930 and Department of Mathematics, Northwest Normal University, Lanzhou, 730070 and Yanqiong Lu and Ruyun and Ma and and 5931 and Department of Mathematics, Northwest Normal University, Lanzhou, 730070 and Ruyun Ma}, 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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