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Hernández M., Eduardo; Henríquez, Hernán R.; McKibben, Mark A.

Existence results for abstract impulsive second-order neutral functional differential equations. (English) Zbl 1173.34049

Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 70, No. 7, 2736-2751 (2009).
The authors provide sufficient conditions for the existence of mild solutions for a class of second order semilinear impulsive neutral functional differential equations with infinite delay in a Banach space. The main results are obtained using the family of bounded linear cosine operators and the fixed point argument. An example is presented showing the applicability of the imposed conditions.
Reviewer: Mouffak Benchohra (Sidi Bel Abbes)

Cited in 42 Documents

MSC:

34K30 Functional-differential equations in abstract spaces
34K40 Neutral functional-differential equations
34K45 Functional-differential equations with impulses

Keywords:

neutral equations; second-order differential equations; impulsive equations; cosine functions of operators
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\textit{E. Hernández M.} et al., Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 70, No. 7, 2736--2751 (2009; Zbl 1173.34049)
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References:

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