Electronic Journal of Differential Equations,
Vol. 2001(2001), No. 24, pp. 1-14.

Title: Existence results for a class of semi-linear evolution equations
        
Author: Eduardo Hernandez M. (Univ. de Sao Paulo, Sao Carlos, SP, Brazil)
          
Abstract: 
 We prove the existence of regular solutions for the
 quasi-linear evolution
 $$ {d \over dt}(x(t)+g(t,x(t))=Ax(t)+f(t,x(t)),
 $$
 where $A$ is the infinitesimal generator of an analytic semigroup
 of bounded linear operators defined on a Banach space  and the functions
 $f, g$ are continuous.
  
Submitted December 14, 2000. Published April 10, 2001.
Math Subject Classifications: 35A05, 34G20, 34A09.
Key Words: Banach spaces; semigroup of linear operators; 
    abstract differential  equations;
    fractional powers of closed operators; regular solutions.