Existence of Mild Solutions for a Semilinear Integrodifferential Equation with Nonlocal Initial Conditions

Carlos Lizama and Juan C. Pozo

Abstract and Applied Analysis, 2012, vol. 2012, issue 1

Abstract: Using Hausdorff measure of noncompactness and a fixed‐point argument we prove the existence of mild solutions for the semilinear integrodifferential equation subject to nonlocal initial conditions u′(t)=Au(t)+∫0tB(t-s)u(s)ds+f(t,u(t)), t ∈ [0,1], u(0) = g(u), where A : D(A)⊆X → X, and for every t ∈ [0,1] the maps B(t) : D(B(t))⊆X → X are linear closed operators defined in a Banach space X. We assume further that D(A)⊆D(B(t)) for every t ∈ [0,1], and the functions f : [0,1] × X → X and g : C([0,1]; X) → X are X‐valued functions which satisfy appropriate conditions.

Date: 2012
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https://doi.org/10.1155/2012/647103

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:647103

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