Existence and Uniqueness of Almost Automorphic Mild Solutions to Some Semilinear Abstract Differential Equations

By Gaston M. N'Guérékata. 2004

94 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/45bfdb2c2bd987fcfe7acd2ba2c14f85ebde99ac

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In Applied Mathematics

In Computational Theory and Mathematics

In Control and Systems Engineering

Citations in the corpus

Bounded mild solutions to fractional integro-differential equations in Banach spaces (2013, methodology): “When a ≡ 0, sufficient conditions for the existence and uniqueness of mild solutions in the cases α = 1, α = 2, with f almost periodic or almost automorphic, among other, have been obtained by several authors in [5, 6, 14, 15, 16, 32] for the case α = 1, and in [5, 21, 34] for α = 2.”
Stepanov-like almost automorphic functions and applications to some semilinear equations (2007, result): “Since the space ASpðXÞ of Stepanov-like almost automorphic functions contains the space AAðXÞ of (Bochner) almost automoprhic functions, it turns out that the main result of this article generalizes the existence results obtained in N’Guérékata [7].”
Pseudo almost automorphic solutions to semilinear differential equations in Banach spaces (2008, background): “From the proof of N’Guerekata [ 5, Theorem 3.2 ], it follows that t → ˜”
Bounded Mild Solutions for Semilinear Integro Differential Equations in Banach Spaces (2010, background): “Remark 3.7. The above corollary generalizes [ 37, Theorem 3.1 ] when Ω = AA(X) and recovers [19, Theorem 2.7] when B = g =0 ; Ω =AAA(X )a nd the remainder cases are new results.”
Almost automorphic solutions for some partial functional differential equations (2007, background): “In [12], the author studied the existence of almost automorphic solutions for the following semilinear abstract differential equation d x(t) = Cx(t) + θ(t, x(t)), for t 0, (1.”