Existence of Solutions in Some Interpolation Spaces for a Class of Semilinear Evolution Equations with Nonlocal Initial Conditions

الملخص EN

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 space X.

Considering the equations in the norm of some interpolation spaces between X and 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.