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Local and global solutions of well-posed integrated Cauchy problems

Pedro J. Miana (2008)

Studia Mathematica

We study the local well-posed integrated Cauchy problem v ' ( t ) = A v ( t ) + ( t α ) / Γ ( α + 1 ) x , v(0) = 0, t ∈ [0,κ), with κ > 0, α ≥ 0, and x ∈ X, where X is a Banach space and A a closed operator on X. We extend solutions increasing the regularity in α. The global case (κ = ∞) is also treated in detail. Growth of solutions is given in both cases.

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