Geodesic
Existence and uniqueness of global solutions for non-autonomous evolution equations with state-dependent nonlocal conditions
Filomat, Tome 37 (2023) no. 3, p. 745

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DOI

In this paper, we consider the existence and uniqueness of global solutions for non-autonomous evolution equations with state-dependent nonlocal conditions, in which the undelayed part admits an evolution operator. We discuss the problems by utilizing theory of evolution operators, Schauder fixed point theorem and Banach fixed point theorem. Some new results on existence and uniqueness of solutions of the considered equation are obtained on the infinite internal [0, +∞). In the end, the obtained results are applied to a class of non-autonomous heat equations with state-dependent nonlocal conditions.
DOI : 10.2298/FIL2303745Z
Classification : 37B55, 47H10, 49J27, 74G25, 74G30
Keywords: Non-autonomous evolution equation, evolution operator, fixed point theorem, state-dependent nonlocal condition 
Jianbo Zhu. Existence and uniqueness of global solutions for non-autonomous evolution equations with state-dependent nonlocal conditions. Filomat, Tome 37 (2023) no. 3, p. 745 . doi: 10.2298/FIL2303745Z
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     title = {Existence and uniqueness of global solutions for non-autonomous evolution equations with state-dependent nonlocal conditions},
     journal = {Filomat},
     pages = {745 },
     year = {2023},
     volume = {37},
     number = {3},
     doi = {10.2298/FIL2303745Z},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2303745Z/}
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