Electronic Journal of Differential Equations, Vol. 2022 (2022), No. 31, pp. 1-14.

Title: Lower and upper solutions for delay evolution equations with nonlocal and
       impulsive conditions
       
Author: Xuping Zhang (Northwest Normal Univ., Lanzhou, China)

Abstract: 
In this article, we apply the method of lower and upper solutions for studying
delay evolution equations with nonlocal and impulsive conditions in infinite
dimensional Banach spaces. Under wide monotone conditions and noncompactness
measure condition of nonlinear term, we obtain the existence of extremal
solutions and a unique solution between lower and upper solutions.
A concrete application to partial differential equations is considered.

Submitted June 2, 2021. Published April 18, 2022.
Math Subject Classifications: 35R12, 35K90, 47D06.
Key Words: Evolution equations; delay; nonlocal and impulsive conditions; 
           lower and upper solutions; measure of noncompactness.