Existence for a class of partial differential equations with nonlocal conditions

This paper is concerned with the existence of mild and classical solutions of nonlocal Cauchy problems. We assume that the linear part generates an analytic compact bounded semigroup, and that the nonlinear part is a Hölder continuous function with respect to the fractional power norm of the linear part. Considering the nonlocal conditions in the αα-norm, we generalize the recent conclusions on this topic. The results obtained will be applied to a class of functional partial differential equations with nonlocal conditions in 12-norm.