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.
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| Xuping Zhang |
Department of Mathematics
Northwest Normal University
Lanzhou 730070, China
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