existence of mild solutions for a semilinear integrodifferential equation with nonlocal initial conditions

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2012
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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.
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lizama2012abstractexistence Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors Carlos Lizama, Juan C. Pozo
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Journal science and technology of advanced materials
Year 2012
DOI
10.1155/2012/647103
URL
http://dx.doi.org/10.1155/2012/647103
Keywords
mathematics

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