“…The approach in Ciprian [13] has been extensively used in the literature concerning the existence and uniqueness of a ‘Lipschitz’ solution for abstract problem with SDA, see, for example, [1–3, 16–18, 31, 32]. A similar regularizing property is used by Rezounenko et al.…”
Section: Introductionmentioning
confidence: 99%
“…In comparison to the early works [13, 24] and the papers [1–4, 13, 16–18, 21, 22, 23–26, 31, 32], we present several novelties. To begin, we prove the existence and ‘uniqueness of a non-Lipschitz’ solution for Equations (1.1)–(1.2).…”
We study the local and global existence and uniqueness of mild solution for a general class of abstract differential equations with state-dependent argument. In the last section, some examples on partial differential equations with state-dependent argument are presented.
“…The approach in Ciprian [13] has been extensively used in the literature concerning the existence and uniqueness of a ‘Lipschitz’ solution for abstract problem with SDA, see, for example, [1–3, 16–18, 31, 32]. A similar regularizing property is used by Rezounenko et al.…”
Section: Introductionmentioning
confidence: 99%
“…In comparison to the early works [13, 24] and the papers [1–4, 13, 16–18, 21, 22, 23–26, 31, 32], we present several novelties. To begin, we prove the existence and ‘uniqueness of a non-Lipschitz’ solution for Equations (1.1)–(1.2).…”
We study the local and global existence and uniqueness of mild solution for a general class of abstract differential equations with state-dependent argument. In the last section, some examples on partial differential equations with state-dependent argument are presented.
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