Existence of Global Mild Solutions for Nonautonomous Abstract Evolution Equations
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)=y0. 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.
Authors
- Yong Zhou (ORCID: https://orcid.org/0000-0002-4099-8077)
- Mian Zhou (ORCID: https://orcid.org/0000-0003-4226-6299)
- Yong Liang (ORCID: https://orcid.org/0000-0002-1449-4182)
Institutions
- Macau University of Science and Technology (MO)
Publication Details
- Journal
- Mathematics
- Published
- 2025-05-23
- DOI
- https://doi.org/10.3390/math13111722
- Citations
- 1
- Primary Topic
- Mathematical and Theoretical Epidemiology and Ecology Models
- Type
- article
- Field-Weighted Citation Impact
- 1.88
Funders
- Fundo para o Desenvolvimento das Ciências e da Tecnologia