Existence of solutions in some interpolation spaces for a class of semilinear evolution equations with nonlocal initial conditions

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. © 2013 jung-chan chang and hsiang liu.