Existence of Global Mild Solutions for Nonautonomous Abstract Evolution Equations
Mian Zhou,
Yong Liang and
Yong Zhou ()
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Mian Zhou: Faculty of Innovation Engineering, Macau University of Science and Technology, Macau 999078, China
Yong Liang: Faculty of Innovation Engineering, Macau University of Science and Technology, Macau 999078, China
Yong Zhou: Faculty of Innovation Engineering, Macau University of Science and Technology, Macau 999078, China
Mathematics, 2025, vol. 13, issue 11, 1-10
Abstract:
In this paper, we investigate the Cauchy problem for nonautonomous abstract evolution equations of the form y ′ ( t ) = A ( t ) y ( t ) + f ( t , y ( t ) ) , t ≥ 0 , y ( 0 ) = y 0 . We obtain new existence theorems for global mild solutions under both compact and noncompact evolution families U ( t , s ) . Our key method relies on the generalized Ascoli–Arzela theorem we previously obtained. Finally, an example is provided to illustrate the applicability of our results.
Keywords: nonautonomous evolution equation; global mild solutions; existence; fixed-point theorem; measure of noncompactness (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:13:y:2025:i:11:p:1722-:d:1663016
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