Existence of solutions for a class of neutral partial differential equations with nonlocal conditions in the αα-norm

This paper is concerned with the existence of mild and strong solutions for some neutral partial differential equations with nonlocal conditions in the αα-norm. The linear part of the equations is assumed to generate a compact analytic semigroup of uniformly bounded linear operators, and the nonlinear part satisfies some Lipschitz conditions with respect to the αα-norm. By using a fixed point theorem of Sadovskii, we establish some existence results, which generalize the recent conclusions on this issue. In the end, the obtained results will be applied to a class of partial differential equations with nonlocal conditions.