Local and global solutions of well-posed integrated Cauchy problems
Pedro J. Miana
Studia Mathematica, Tome 187 (2008), p. 219-232 / Harvested from The Polish Digital Mathematics Library
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We study the local well-posed integrated Cauchy problem v'(t)=Av(t)+(tα)/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.

Publié le : 2008-01-01
EUDML-ID : urn:eudml:doc:286353 
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Pedro J. Miana. Local and global solutions of well-posed integrated Cauchy problems. Studia Mathematica, Tome 187 (2008) pp. 219-232. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm187-3-2/