Existence of Solutions in Some Interpolation Spaces for a Class of Semilinear Evolution Equations with Nonlocal Initial Conditions
Keyword(s):
This paper is concerned with the existence of mild and strong solutions for a class of semilinear evolution equations with nonlocal initial conditions. The linear part is assumed to be a (not necessarily densely defined) sectorial operator in a Banach spaceX. Considering the equations in the norm of some interpolation spaces betweenXand the domain of the linear part, we generalize the recent conclusions on this topic. The obtained results will be applied to a class of semilinear functional partial differential equations with nonlocal conditions.
2020 ◽
Vol 21
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pp. 829-841
2013 ◽
Vol 18
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pp. 599-611
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2015 ◽
Vol 195
(5)
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pp. 1639-1658
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