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.