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Volume 55, Issue 4
Monotone Iterative Technique for $S$-Asymptotically Periodic Problem of Evolution Equation with Delay

Qiang Li & Hong Qiao

DOI: 10.4208/jms.v55n4.22.03

J. Math. Study, 55 (2022), pp. 381-397.

Published online: 2022-11

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  • Abstract

This paper is concerned with $S$-asymptotically periodic problem of evolution equation with delay in ordered Banach space. Under some weaker assumptions, we construct monotone iterative method in the presence of the lower and upper solutions to the delayed evolution equation, and obtain the existence of maximal and minimal $S$-asymptotically periodic mild solutions. Finally, we give an example to exhibit the practicability of our abstract results.

  • Keywords

Evolution equation, delay, $S$-asymptotically periodic mild solutions, monotone iterative technique, positive C$_0$-semigroup.

  • AMS Subject Headings

47J35, 34K30, 34K13, 47D06, 47D60

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

lznwnuliqiang@126.com (Qiang Li)

1808192113@qq.com (Hong Qiao)

  • BibTex
  • RIS
  • TXT
@Article{JMS-55-381, author = {Li , Qiang and Qiao , Hong}, title = {Monotone Iterative Technique for $S$-Asymptotically Periodic Problem of Evolution Equation with Delay}, journal = {Journal of Mathematical Study}, year = {2022}, volume = {55}, number = {4}, pages = {381--397}, abstract = {

This paper is concerned with $S$-asymptotically periodic problem of evolution equation with delay in ordered Banach space. Under some weaker assumptions, we construct monotone iterative method in the presence of the lower and upper solutions to the delayed evolution equation, and obtain the existence of maximal and minimal $S$-asymptotically periodic mild solutions. Finally, we give an example to exhibit the practicability of our abstract results.

}, issn = {2617-8702}, doi = {https://doi.org/10.4208/jms.v55n4.22.03}, url = {http://global-sci.org/intro/article_detail/jms/21160.html} }
TY - JOUR T1 - Monotone Iterative Technique for $S$-Asymptotically Periodic Problem of Evolution Equation with Delay AU - Li , Qiang AU - Qiao , Hong JO - Journal of Mathematical Study VL - 4 SP - 381 EP - 397 PY - 2022 DA - 2022/11 SN - 55 DO - http://doi.org/10.4208/jms.v55n4.22.03 UR - https://global-sci.org/intro/article_detail/jms/21160.html KW - Evolution equation, delay, $S$-asymptotically periodic mild solutions, monotone iterative technique, positive C$_0$-semigroup. AB -

This paper is concerned with $S$-asymptotically periodic problem of evolution equation with delay in ordered Banach space. Under some weaker assumptions, we construct monotone iterative method in the presence of the lower and upper solutions to the delayed evolution equation, and obtain the existence of maximal and minimal $S$-asymptotically periodic mild solutions. Finally, we give an example to exhibit the practicability of our abstract results.

Qiang Li & Hong Qiao. (2022). Monotone Iterative Technique for $S$-Asymptotically Periodic Problem of Evolution Equation with Delay. Journal of Mathematical Study. 55 (4). 381-397. doi:10.4208/jms.v55n4.22.03
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