Integral inequalities and mild solutions of semilinear neutral evolution equations

Existence of mild solutions to semilinear neutral evolution equations with nonlocal conditions is proved. The result is obtained by using fractional power of operators, Krasnoselski–Schaefer type fixed point theorem and by applying a modification of the Bihari type inequality to the case of singular integral inequality. An application to partial differential equations is given.  2004 Elsevier Inc. All rights reserved.