Publication Date:
2015-08-20
Description:
The aim of the paper is to provide, by an approach based on the Mönch fixed point theorem, existence results for the semilinear evolution problem with distributed measures{ d x = ( − A x + f ( t , x ) ) d t + d g , t ∈ [ 0 , 1 ] , x ( 0 ) = x 0 ,where −A is the infinitesimal generator of a (uniformly or strongly) continuous semigroup { T ( t ) , t ≥ 0 } of bounded linear operators, f is not necessarily continuous and g : [ 0 , 1 ] → X is a regulated function.Working with Kurzweil-Stieltjes integrals and using a measure of non-compactness allows us to relax the assumptions on the semigroup, on f and g comparing to some already known results.MSC: 37L05, 47D06, 47J35, 58D25, 26A42, 47H10.
Print ISSN:
1687-1820
Electronic ISSN:
1687-1812
Topics:
Mathematics
Permalink