Monotone iterative technique for evolution equations with delay and nonlocal conditions in ordered Banach space

Abstract

In this paper, based on monotone iterative method in the presence of the lower and upper solutions, we investigate the existence and uniqueness of the S-asymptotically ω-periodic mild solutions to a class of nonlocal problems of evolution equations with delay in ordered Banach spaces. Firstly, we introduce the concept of lower S-asymptotically ω-periodic solution and upper S-asymptotically ω-periodic solution. Secondly, we construct monotone iterative method in the presence of the lower and upper solutions to evolution equations with delay, and obtain the existence of maximal and minimal S-asymptotically ω-periodic mild solutions for the mentioned system under wide monotone conditions and noncompactness measure condition of nonlinear term. Finally, as the application of abstract results, an example is given to illustrate our main results.

Keywords:

• Evolution equations
• delay
• nonlocal problems
• monotone iterative technique
• $C_0$-semigroup
• S-asymptotically ω-periodic mild solutions

Mathematics Subject Classifications:

• 35R12
• 35K90
• 47D06

Data availability statement

My manuscript has no associate data.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This research was supported by the National Natural Science Foundation of China [No. 12061062], Science Research Project for Colleges and Universities of Gansu Province [No. 2022A-010].