Abstract.
We study the existence of mild solutions for semilinear differential equations with nonlocal initial conditions in a separable Banach space X. We derive conditions in terms of the Hausdorff measure of noncompactness under which mild solutions exist in Lp(0, b; X). For illustration, a partial integral differential system is worked out.
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Dedicated to Felix Browder on his 80th birthday
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Xue, X. Lp theory for semilinear nonlocal problems with measure of noncompactness in separable Banach spaces. J. fixed point theory appl. 5, 129–144 (2009). https://doi.org/10.1007/s11784-008-0090-5
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DOI: https://doi.org/10.1007/s11784-008-0090-5