We establish averaging results for semilinear functional-differential equations with infinite delay in an abstract phase space of axiomatically defined Banach space-valued functions, where the unbounded linear part generates a noncompact semigroup and the nonlinear part satisfies a condition with respect to the second argument, which is weaker than the ordinary Lipschitz condition. As a preliminary result, by using the technique of the theory of condensing maps, we establish a theorem on existence and uniqueness of mild solutions for equations of this kind.
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Published in Neliniini Kolyvannya, Vol. 24, No. 1, pp. 62–82, January–March, 2021.
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Guedda, L., Ouardani, A. On the Averaging Principle for Semilinear Functional Differential Equations with Infinite Delay in a Banach Space. J Math Sci 265, 629–650 (2022). https://doi.org/10.1007/s10958-022-06071-9
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DOI: https://doi.org/10.1007/s10958-022-06071-9