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Second order abstract differential equations of elliptic type set in R+

Eltaief A., Maingot S.

Demonstratio Mathematica

2013

Vol. 46, nr 4

709--727

In this paper we give some new results on complete abstract second order differential equations of elliptic type set in R+. In the framework of UMD spaces, we use the celebrated Dore-Venni Theorem to prove existence and uniqueness for the strict solution. We will use also the Da Prato-Grisvard Sum Theory to furnish results when the space is not supposed to be a UMD space.